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JAN  12 


THE  PSYCHOLOGICAL  METHODS  OF  TESTING 
INTELLIGENCE 


jflonograpfya 


lw  (fim\  Mantroee 
No.   13 


THE  PSYCHOLOGICAL  METHODS 
OF  TESTING  INTELLIGENCE 


By 
WILLIAM  STERN 


TRANSLATED  FROM  THE  GERMAN 
BY 

GUY  MONTROSE  WHIPPLE 

Assistant  Professor  of  Educational  Psychology 
Cornell  University. 


BALTIMORE 

WARWICK  &  YORK,  Inc. 

1914 


Copyright,  1914 
By  WARWICK  &  YORK,  Inc. 


C  6 


CONTENTS 

Author's  Preface v 

Translator's  Preface ix 

Introduction :  Nature  and  Problem  of  Intelligence  Testing 1 

1.  Intelligence  and  Intelligence  Testing .'" '  ••  Jt 

2.  Practical  Problems  of  Intelligence  Testing 5 

I.  Single  Tests  and  Series  of  Tests 13 

1.  Single  Tests 13 

2.  The  Inadequacy  of  the  Single  Test 18 

3.  Series  of  Tests 23 

II.  The  Method  of  Age-Gradation  (Binet-Simon  Method) 29 

1.  The  Principle  of  the  Method  and  the  Tests  Employed.  29 

2.  The  Resultant  Values  (Mental  Age,  etc.) 36 

3.  Results  with  Normal  Children 42 

(a)  General  Distribution  of  the  Level  of  Intelligence.  43 

(b)  Different  Age-Levels  and  Nationalities 46 

(c)  Children  of  Different  Social  Strata 50 

(d)  Intelligence  and  School  Performance 51 

(e)  Sex  Differences 65 

(f )  Repeated  Tests  with  the  Same  Children 68 

4.  Abnormal  Children 70 

(a)  Mental   Arrest  and   Retardation.    Mental   Quo- 
tient    70 

(b)  Relation  to  the  Several  Tests 85 

(c)  Intelligence  and  School  Ability 90 

5.  Points  of  View  for  the  Reorganization  and  Improve- 

ment of  the  Gradation  Method 91 

(a)    Selection  and  Appraisement  of  the  Tests 92 

iii 


79 


iv  CONTENTS. 

(b)  The  Composition  of  Series  for  the  Several  Years.     99 

(c)  The  Extension  of  the  System 101 

(d)  The  Computation  of  the  Final  Values 104 

III.     Estimation  and  Testing  of  Finer  Gradations  of  Intelli- 
gence ( Method  of  Ranks) 109 

1.  The  Problem 109 

2.  The  Teacher's  Estimation  of  Intelligence 116 

3.  Estimated  Intelligence  and  School  Performance 127 

4.  Rank-Orders  of  Intelligence  Obtained  by  Tests i35 


Bibliography 147 

Appendix  1 155 

Appendix  II 156 

Index    .  .  159 


AUTHOR'S   PREFACE 

I  undertook  for  the  last  German  congress  of  psy- 
chology, held  at  Berlin,  April,  1912,  a  general  review 
of  the  psychological  methods  of  testing  intelligence. 
As  I  had  only  an  hour  at  my  disposal  in  my  address, 
I  could  at  that  time  do  little  more  than  outline  cer- 
tain of  the  main  features  of  this  very  broad  field.  It 
seemed  to  me,  however,  hardly  desirable  to  publish 
the  address  in  the  form  in  which  it  was  given.  I 
felt,  on  the  contrary,  that  in  view  of  the  now  ever- 
increasing  interest  displayed  in  the  theme  both  in 
Germany  and  elsewhere  and  in  view  of  the  extraordi- 
narily scattered  nature  of  the  literature — much  of 
which,  by  the  way,  is  difficult  of  access — that  an  ex- 
position of  the  topic  on  a  wider  scale  was  demanded. 
So  I  have  tried  to  elaborate  my  original  review  to 
this  larger  scale.  I  have  treated  in  it  three  main 
topics:  single  tests,  the  serial  method  (after  Binet- 
Simon)  and  the  methods  of  correlation  and  estima- 
tion. 

In  the  form  of  my  treatment,  also,  I  have  over- 
stepped the  bounds  of  the  mere  * ;  general  review. ' '  I 
have  not  confined  myself  to  setting  down  what  now 
exists,  but  have  myself  taken  an  attitude  toward  the 
problem,  have  offered  criticisms  of  the  methods  and 


VI      PSYCHOLOGICAL   METHODS  OP   TESTING   INTELLIGENCE 

made  proposals  for  their  modification  and  develop- 
ment. In  making  these  criticisms  and  suggestions  I 
have  been  able  to  use  the  experience  that  has  come 
from  the  tests  of  intelligence  which  have  been  in 
progress  at  Breslau  for  some  years  past.  Many  of 
these  experiments,  in  which  psychologists,  educators 
and  physicians  have  cooperated  in  a  gratifying 
manner,  have  already  been  published;  others  are 
still  in  progress.  Yet,  thanks  to  the  courtesy  of  these 
workers,  I  am  able  to  make  a  preliminary  report  of 
some  of  these  as  yet  unfinished  investigations.  I 
have  also  taken  the  opportunity  to  incorporate  some 
minor  contributions  to  the  problem  that  have  origi- 
nated in  the  exercises  of  the  Psychological  Seminary 
at  Breslau. 

The  subject  under  discussion  is  limited  to  some 
extent  by  the  circumstance  that  tests  of  intelligence 
have  been  almost  always  restricted  to  children  and 
youths.  But  it  is  just  the  peculiarity  of  the  psycho- 
logical methods  of  intelligence  testing — psycholog- 
ical in  the  narrower  sense,  in  contrast,  e.  g.,  to  the 
psychiatrical  methods — that  they  take  their  start 
from  the  mental  life  of  the  child,  though  later,  of 
course,  the  attempt  is  made  to  carry  them  over  into 
test  methods  for  adults.  On  this  account  I  have 
treated  in  some  detail  the  results  that  accrue  to  peda- 
gogy, and  not  only  to  the  pedagogy  of  auxiliary 
classes  and  of  the  subnormal  child,  but  also  to  the 
pedagogy  of  the  normal  child. 

In  my  judgment,  intelligence  testing  is  one  of  the 
most  promising  fields  of  applied  psychology,  using 
that  term  in  the  strictest  sense.  For  this  reason  I 
wanted  to  make  this  survey  of  it  accessible  to  wider 


AUTHOR'S  PREFACE  vii 

circles  of  readers  outside  the  psychological  profes- 
sion, especially  to  teachers  of  normal  and  of  back- 
ward children,  to  school  administrative  authorities, 
to  school  physicians,  to  specialists  in  nervous  and  in 
children's  diseases,  and  to  those  engaged  in  child 
welfare  work.  This  special  edition,  accordingly,  has 
been  arranged.  I  hope  that  it  will  demonstrate  to 
the  workers  in  these  circles  the  great  importance  and 
fruitfulness  of  the  psychologist's  methods  and  at  the 
same  time  show  them  the  difficulties  and  the  gaps  in 
the  present  status  of  this  work,  and  that  so  plainly 
as  to  prevent  overhasty  attempts  at  practical  appli- 
cation. 

W.  STEEN. 
Breslau,  October,  1912. 


TRANSLATOR'S  PREFACE 

This  translation  of  Stern's  Die  psychologischen 
Methoden  der  Intelligenzprufung  has  been  under- 
taken because  the  monograph,  though  dealing  with  a 
different  topic,  aims,  like  my  previous  translation  of 
Offner's  Mental  Fatigue,  to  collate,  systematize  and 
appraise  a  mass  of  scattered  and  to  most  readers  in- 
accessible material  that  bears  upon  a  problem  of  un- 
questioned importance. 

Professor  Stern  was  one  of  the  pioneers  and  most 
active  expositors  of  the  investigation  of  the  psychol- 
ogy of  testimony,  for  the  furtherance  of  which  he  in- 
stituted a  new  periodical,  Beitrdge  zur  Psychologic 
der  Aussage,  which  was  later  enlarged  to  cover  the 
wider  field  of  applied  psychology  in  general  (Zeit- 
schrift  fur  angewandte  Psychologie}.  Stern  is  like- 
wise well-known  for  his  contributions  to  individual 
psychology,  notably  for  his  important  work  on  indi- 
vidual differences  ( Ueber  Psychologie  der  individuel- 
len  Differ  enzen),  published  originally  in  1900  and 
completely  rewritten  in  1911  under  the  title,  Die  dif- 
ferentielle  Psychologie,  and  for  his  numerous  sig- 
nificant contributions  to  the  psychology  of  childhood. 
From  his  Psychological  Seminary  at  Breslau  have 
appeared  many  researches,  some  of  which  are  re- 

ix 


X       PSYCHOLOGICAL    METHODS   OF   TESTING   INTELLIGENCE 

ported  for  the  first  time  in  the  present  monograph. 
In  conjunction  with  Lipmann  he  has  also  founded  the 
Institut  fur  angewandte  Psychologic,  which  aims  to 
serve  as  a  museum  and  clearing  house  for  the  col- 
lection and  dissemination  of  methods  and  materials 
for  studying  and  recording  the  mental  processes  of 
individuals  and  for  facilitating  the  application  of 
psychology  to  various  practical  problems. 

What  Stern  has  aimed  to  do  in  the  present  mono- 
graph is  sufficiently  set  forth  in  his  own  preface,  but 
it  may  be  added  here  that  his  book  affords  what  is, 
so  far  as  I  know,  the  best,  and  in  fact  almost  the  only 
authoritative,  critical  and  compact  general  survey 
of  the  literature  of  intelligence  testing  which  is 
adapted  for  lay  readers  as  well  as  for  professional 
psychologists. 

In  perfecting  this  translation  I  have  received  much 
valuable  aid  from  the  members  of  my  class  in  Ger- 
man Educational  Psychology,  in  which  the  mono- 
graph was  used  as  a  text,  and  from  my  colleagues, 
Professor  P.  K.  Pope,  of  the  German  Department, 
and  Mr.  D.  K.  Eraser,  assistant  in  Educational  Psy- 
chology. 

GUY  MONTBOSE  WHIPPLE. 

Cornell  University,  January  1st,  1914. 


THE  PSYCHOLOGICAL  METHODS  OF  TESTING 
INTELLIGENCE 


INTRODUCTION 
Nature  and  Problem  of  Intelligence  Testing 

1.    Intelligence  and  Intelligence  Testing 

Modern  experimental  psychology,  which  started 
with  the  study  of  sense-perception  and  then  under- 
took that  of  ideas  and  feelings,  has  in  the  last  decade 
begun  to  deal  with  intellectual  functions  themselves. 
And  it  is  worthy  of  note  that  general  theoretical  psy- 
chology and  differential  applied  psychology  took  this 
step  forward  at  the  same  time,  though  for  the  most 
part  independently.  In  the  former  there  was  devel- 
oped a  psychology  of  thinking,  in  the  latter  there 
appeared  the  investigation  of  differences  in  intelli- 
gence. 

Our  discussion  must  be  restricted  to  the  second 
problem  with  which  alone  we  are  concerned.  To  the 
other  branch  of  psychology  we  may  confidently  leave 
the  question  of  the  general  nature  of  intellectual  ac- 
tivity and  the  investigation  of  the  phenomena  that 
constitute  thinking  as  such.  What  we  are  interested 
in  is  not  intelligence  as  a  phenomenon,  but  intelli- 
gence as  a  capacity  and  particularly  a  capacity  with 
respect  to  which  men  differ  one  from  another.  And 
intelligence  testing  is  the  determination  of  the  de- 
gree of  this  capacity  in  a  given  individual.  , 


2        PSYCHOLOGICAL   METHODS  OP   TESTING   INTELLIGENCE 

The  objection  is  often  made  that  the  problem  of 
intellectual  diagnosis  can  in  no  way  be  successfully 
dealt  with  until  we  have  exact  knowledge  of  the  gen- 
eral nature  of  intelligence  itself.  But  this  objection 
does  not  seem  to  me  pertinent.  In  science  there  is  no 
such  precise  sequence  of  the  different  research  prob- 
lems. We  measure  electro-motive  force  without 
knowing  what  electricity  is,  and  we  diagnose  with 
very  delicate  test  methods  many  diseases  the  real 
nature  of  which  we  know  as  yet  very  little.  Indeed, 
it  may  be  asserted,  quite  on  the  contrary,  that  prog- 
ress in  testing  intelligence  may  shed  light  from  a  new 
angle  upon  the  theoretical  study  of  intelligence  and 
thus  supplement  the  psychology  of  thinking  in  a 
valuable  manner.  If  it  turns  out,  for  instance,  that 
certain  symptoms  are  relevant  and  others  irrelevant 
for  the  differentiation  of  the  intelligence  shown  by 
different  persons ;  if,  again,  one  series  of  these  symp- 
toms exhibit  a  high  degree,  another  series  a  less  de- 
gree of  intercorrelation,  then  our  knowledge  of  the 
structure  of  intelligence  must  thereby  be  little  by  lit- 
tle increased,  and  thus  there  will  develop  a  fruitful 
reciprocity  between  the  two  phases  of  investigation, 
theoretical  and  applied. 

Naturally,  we  cannot  begin  our  work  without  a  pre- 
liminary definition  of  intelligence,  however  pro- 
visional it  may  be.  And  this  definition  must  be 
neither  too  broad  nor  too  narrow. 

Many  psychiatrists  have  used  a  definition  of  intel- 
ligence that  is  too  broad.  They  use  intelligence,  in 
fact,  to  include  mental  attainments  of  all  kinds,  all 
those  mental  qualities,  then,  that  are  not  volitional 
or  emotional.  If  this  position  be  taken,  it  follows, 


NATURE  AND  PROBLEM   OF   INTELLIGENCE  TESTING  3 

evidently  that  the  examination  of  immediate  mem- 
ory, of  ability  to  learn,  of  range  of  information,  of 
fidelity  of  report,  or  of  discriminative  sensitivity  is 
just  as  much  a  constituent  part  of  intelligence  testing 
as  the  examination  of  ability  to  apprehend,  to  syn- 
thetize,  of  capacity  to  judge,  to  conclude,  to  define, 
to  criticize,  etc.  Again,  a  question  that  is  very  im- 
portant for  us,  viz. :  to  what  extent  intelligence  really 
enters  into  these  first-named  activities,  and  whether 
and  in  what  way  it  shows  signs  of  its  presence  in 
them,  becomes  absurd.  But  the  advance  made  in  the 
recent  development  of  intelligence  testing,  in  con- 
trast to  the  uncritical  determination  of  mental  level 
by  any  sort  of  questions  and  tests,  consists  in  the 
fact  that  we  not  only  limit  intelligence  by  setting  it 
over  against  the  emotive  and  volitional  nature  of 
an  individual,  but  also  ascribe  to  it  a  definitely  re- 
stricted place  within  the  mental  functions. 

This  delimitation  of  the  sphere  of  intelligence  that 
is  even  now  essential  cannot  be  effected,  in  my  opin- 
ion, from  a  phenQmenoloffical,  but  only  from  a  tele- 
ological  point  of  view.  In  fact,  my  definition  is  this : 

Intelligence  is  a  general  capacity  of  an  individual 
consciously  to  adjust  his  thinking  to  new  require- 
ments:^ is  general  mental  adaptability  to  new  prob- 
lems and  conditions  of  life. 

This  definition  differentiates  intelligence  clearly 
from  other  mental  capacities. 

The  fact  that  the  adjustment  is  made  to  the  new 
distinguishes  intelligence  from  memory  whose  fun- 
damental teleologicgl feature  is  the  conservation  and 
utilization  of  conscious  contents  already  given. 

The  fact  of  adaptation,  again,  emphasizes  the  de- 


4        PSYCHOLOGICAL    METHODS   OF  TESTING   INTELLIGENCE 

pendence  of  the  performances  upon  external  factors, 
on  the  problems  and  demands  of  life,  and  thus  dis- 
tinguishes intelligence  from  genius,  whose  nature  is 
to  create  the  new  spontaneously. 

Finally,  the  fact  that  the  capacity  is  a  general 
capacity  distinguishes  intelligence  from  talent  the 
characteristic  of  which  is  precisely  the  limitation  of 
efficiency  to  one  kind  of  content.  He  is  intelligent, 
on  the  contrary,  who  is  able  easily  to  effect  mental 
adaptation  to  new  requirements  under  the  most 
varied  conditions  and  in  the  most  varied  fields.  If 
talent  be  a  material  efficiency,  intelligence  is  a  formal 
efficiency. 

I  trust  that  these  distinctions  may  serve  to  lessen 
the  confusion  that  has  been  current.  It  is  not  so  long 
ago,  indeed,  that  in  psychiatry  'information  tests' 
were  carried  on  as  'intelligence  tests,'  thereby  con- 
fusing memory  and  intelligence.  And  we  often,  even 
nowadays,  find  intelligence  and  talent  confused  in 
everyday  life.  In  the  school,  for  instance,  a  teacher 
of  a  special  subject  like  mathematics,  who  perceives 
the  special  gift  of  a  pupil  in  that  field,  may  easily 
come  to  believe  without  further  evidence  that  this 
pupil  has  general  ability,  or  in  other  words,  to  rate 
him  as  an  intelligent  pupil. 

But  we  should  not  interpret  this  delimitation  to 
mean  the  erection  of  sharply  distinct  faculties,  as  in 
the  old  faculty  theory.  Intelligence,  for  instance, 
does  not  function  by  itself  and  memory  by  itself; 
rather,  every  operation  of  memory  is  more  or  less 
impregnated  with  intellectual  functions  and  vice 
versa:  the  extent  of  this  interconnection  can  be  indi- 
cated only  by  the  correlation  of  the  tested  symptoms. 


NATURE   AND  PROBLEM   OF   INTELLIGENCE  TESTING  5 

But  just  on  account  of  this  composite  character  of 
every  actual  mental  process  it  seems  to  me  that  the 
definition  of  intelligence  I  have  given  above  is  indis- 
pensable as  a  regulative  principle  for  further  investi- 
gation :  I  mean  that  any  sort  of  perceptive,  memorial 
or  attentive  activity  is  at  the  same  time  an  intelli- 
gent activity  just  in  so  far  as  it  includes  a  new  adjust- 
ment to  new  demands. 

We  must  add  one  final  limitation :  we  are  consid- 
ering only  those  phases  of  intelligence  testing  that 
deal  with  a  scale  of  degrees.  This  does  not  mean  to 
minimize  in  the  slightest  the  importance  of  qualita- 
tive differences  in  types  of  intelligence  (analytic- 
synthetic,  objective-subjective,  etc.) ;  we  need  only 
refer  to  the  importance  of  the  essay  as  a  means  of 
testing  for  these  phases.1  But  we  shall  discuss  in 
this  monograph  only  those  forms  of  procedure  that 
permit  us  to  say  of  a  given  person  that  his  intelli- 
gence is  of  such  and  such  degree. 

As  the  title  of  the  book  indicates,  the  problem  of 
method  will  be  prominent  throughout  our  presenta- 
tion. We  can  thus  best  do  justice  to  the  present 
status  of  the  question,  for  the  significance  of  the  re- 
sults thus  far  obtained  lies  particularly  in  the  fact 
that  they  serve  to  provide  new  suggestions  for  the 
perfecting  of  our  methods. 

2.    Practical  Problems  of  Intelligence  Testing 

Since  we  have  to  do  here  not  with  methods  de- 
signed for  purely  theoretical  investigations,  but  with 

*On  this  aspect  of  intelligence,  consult  the  general  review  and 
bibliography  given  in  my  earlier  discussion  (1:  pp.  203-218,  433-4). 

[Note :  numbers  in  parentheses  refer,  unless  otherwise  indicated, 
to  the  reference  list  at  the  end  of  this  monograph. — Translator.] 


6       PSYCHOLOGICAL    METHODS   OF   TESTING   INTELLIGENCE 

methods  that  are  to  be  employed  in  daily  life,  their 
form  is  determined,  at  least  in  part,  by  the  practical 
needs  that  are  to  be  satisfied  by  intelligence  testing. 
We  must  distinguish  four  groups  that  arise  from  the 
combination  of  the  two  pairs  of  terms :  abnormal  and 
normal,  adult  and  child.2 

(a)  Adult,  abnormal  individuals  form  the  chief 
material  of  the  psychiatrists,  who  in  consequence 
were  the  first  to  want  to  test  intelligence.3  Not  only 
have  they  invented  single  methods,  but  they  have  also 
devised  whole  series  or  systems  of  examination 
(Eieger,  Kraepelin,  Sommer,  Ziehen,  Gregor,  Bern- 
stein, Rossolimo,  et  al.)  The  contents  of  these  sys- 
tems are  such  as  to  bring  them  only  partially  within 
our  scope;  by  far  the  greater  portion  of  them  take 
on  the  character  of  questions  and  qualitative  tests 
rather  than  that  of  quantitatively  gradable  tests; 
even  where  these  latter  have  been  used,  comparative 
material  for  normal  persons  is  often  enough  want- 
ing. Whether  the  outcome  of  any  one  of  these  tests 
might  really  indicate  an  abnormally  weak  intelligence 
was  frequently  judged  on  the  basis  of  a  preconceived 
opinion  as  to  how  normal  men  might  be  expected  to 
react  to  the  test  in  question.  In  recent  years  this 
has  been  remedied.  Kodenwald  (22)  showed  with 
regard  to  a  group  of  information  tests  how  much  of 
what  had  a  priori  been  deemed  abnormal  really  lay 
within  the  bounds  of  normality.  Many  psychiatrists 
have  sought  to  obtain  comparative  standards  for 

2A  similar  division  is  used  by  Meumann  (15),  though  he,  to  be 
sure,  defines  intelligence  somewhat  more  broadly  than  do  we. 

*An  extensive  general  summary  of  the  more  important  methods 
of  intelligence  testing  used  by  alienists  will  be  found  in  Jaspers 
(12). 


NATURE   AND  PROBLEM    OF   INTELLIGENCE  TESTING  7 

their  methods  by  extensive  application  of  them  to 
normal  persons  (Sommer,  26;  Ziehen,  30;  Eansch- 
burg;  Kossolimo,  23-25).  Others  have  turned  to  ac- 
count the  fact  that  certain  methods  had  already 
been  tried  out  extensively  by  psychologists  upon 
normal  persons,  e.  g.,  Ebbinghaus'  completion 
method,  the  report  experiment.4  But  how  far  all  this 
comes  from  meeting  the  need  of  the  alienist  himself 
is  shown  by  the  decision  of  the  International  Con- 
gress of  Physicians  to  turn  to  the  psychologists  in 
order  to  secure  normal  series  for  the  various  psy- 
chiatrical tests  of  intelligence.  This  task  has  been 
undertaken  by  the  Institute  for  Applied  Psychology. 

(6)  Abnormal  children  have  become,  just  in  the 
last  few  decades,  a  center  of  pedagogical,  socio-polit- 
ical, and  medical  interest.  The  whole  pedagogy  of 
the  subnormal,  the  schema  of  auxiliary  schools  and 
special  classes,  the  juvenile  court  and  the  various 
protective  and  corrective  institutions  are,  indeed, 
matters  of  very  recent  development,  but  they  are  de- 
manding a  more  exact  study  of  the  individuality  of 
the  child,  both  for  purposes  of  mental  diagnosis  and 
for  *  psycho  technic'  purposes  (training,  treatment, 
punishment,  etc.).  To  meet  these  needs,  the  determi- 
nation of  degree  of  intelligence  is,  though  not  the 
only,  at  least  a  most  important  factor. 

The  weaknesses  of  the  psychiatrical  methods  men- 
tioned above  were  doubled  when  these  methods  were 
applied  to  these  new  problems.  With  adults  we  knew 
little  enough  of  the  normal  standard  to  which  the  per- 
formances of  abnormal  subjects  were  to  be  com- 

*For  a  general  account  of  these  methods,  see  the  translator's 
Manual  of  Mental  and  Physical  2'ests,  Baltimore,  2d  ed.,  1914. 


8       PSYCHOLOGICAL   METHODS  OF  TESTING   INTELLIGENCE 

pared,  but  with  children  we  knew  nothing  at  all. 
What  is  more,  one  normal  standard  is  not  enough  in 
this  case ;  every  age-year  must  have  its  own  standard. 
The  magnitude  of  a  defect  of  intelligence  in  a  nine- 
year  old  child  can  be  determined  only  by  comparing 
it  with  the  normal  nine-year  old  intelligence,  and  so 
with  other  ages.  The  consequent  demand  for  the 
creation  of  normal  test-series  for  each  year  of  child- 
hood was  met,  as  a  matter  of  fact,  not  from  the  side  of 
psychiatry,  but  from  that  of  psychology.  Alfred 
Binet,  with  the  cooperation  of  the  physician,  Simon, 
has  created  such  a  graded  series  of  tests;  and  al- 
though the  system  as  it  now  stands  may  be  far  from 
final,  its  fundamental  conception  will  retain  its  per- 
manent value  and  will  doubtless  lead  us  ultimately  to 
a  completely  satisfactory  solution.  His  method  has 
already  attained  international  usage.  We  shall  dis- 
cuss it  fully  in  the  second  part  of  our  treatment. 

(c)  Normal  children  and  youths.  It  is  not  to  be 
supposed,  however,  that  intelligence  testing  of 
normal  children  has  merely  the  secondary  import- 
ance of  supplying  standards  of  comparison  for  in- 
vestigations of  the  feeble-minded.  On  the  contrary, 
the  gradation  of  intelligence  within  the  range  of 
normality  is  an  entirely  independent  problem  that  is 
closely  connected  with  practical  pedagogical  inter- 
ests. The  ordinary  school  examinations  afford  a 
notion  of  the  pupil's  knowledge  and  of  his  external 
accomplishments,  but  they  do  not  afford  an  index 
of  his  inner  endowment,  of  his  mental  maturity  and 
power ;  it  is  here  that  psychological  tests  must  sup- 
plement other  forms  of  examination.  This  need  is 
especially  evident  at  entrance  examinations,  but  it 


NATURE  AND  PROBLEM   OF  INTELLIGENCE  TESTING 

exists  within  the  ordinary  administration  of  the 
school  as  well,  for  the  demand,  nowadays  so  em- 
phatically voiced,  that  instruction  shall  be  individ- 
ualized to  the  fullest  possible  extent,  presupposes 
a  fuller  insight  into  the  nature  of  individualities. 
Very  recently,  in  fact,  serious  attempts  have  been 
made  to  make  divisions  into  classes  and  sections  on 
a  psychological  and  qualitative  basis  (special  classes 
for  the  subnormal,  classes  for  the  backward,  sepa- 
rate classes  for  the  specially  gifted,  *  parallel' 
classes  with  normal  and  minimal  courses  of  instruc- 
tion for  pupils  of  different  degrees  of  ability  in  par- 
ticular subjects) — attempts  that  demand,  as  an  in- 
dispensable prerequisite  the  possibility  of  very  ex- 
act determination  of  the  actual  degree  of  mental 
ability.5 

In  this  connection  we  must,  of  course,  guard 
against  the  danger  which  is  apt  to  arise  of  suppos- 
ing that  we  have  grasped  the  individuality  of  a  pupil 
in  its  totality  when  we  have  tested  his  intelligence. 
The  fact  that  intelligence  can  be  more  easily  treated 
quantitatively  than  can  other  individual  capacities 
must  not  lead  us  to  overestimate  its  import.  Never- 
theless, the  fact  that  we  can  deal  with  intelligence  by 
itself  does  serve  to  disclose  the  structure  of  the  in- 
dividuality. We  can  determine  whether  a  per  form - 


'All  these  pedagogical  reform-movements  that  are  related  to  the 
problem  of  intelligence  were  the  general  subject  of  discussion  at 
the  first  German  Congress  for  Child  Training  and  Paidology 
(Kongress  f«r  Jugendbildung  tind  Jugendkunde)  that  it  was  con- 
ducted by  the  School  Reform  Association  (Bund  fur  Schulreform) 
at  Dresden,  1911.  The  addresses  and  discussions  of  this  congress 
have  been  published  in  separate  form  (11)  :  the  special  problem  of 
testing  intelligence  was  discussed  in  the  addresses  of  Meumann, 
Kramer,  and  the  author. 


10     PSYCHOLOGICAL    METHODS   OP   TESTING    INTELLIGENCE 

ance  of  greater  or  lesser  degree  depends  on  talent  f 
or  on  intelligence;  we  can  investigate  what  degree 
of  correspondence  exists  between  the  experimental 
results  and  the  teachers'  judgments  of  the  intelli- 
gence of  pupils;  we  can  delimit  the  extent  to  which 
general  school  efficiency  is  dependent  on  intelligence 
itself  on  the  one  hand  and  on  non-intellectual  factors 
on  the  other  hand — a  delimitation  that,  as  will  be 
shown  later,  forms  one  of  the  chief  merits  of  the 
psychological  methods. 

The  studies  of  normal  children  that  bear  directly 
upon  our  problem  were  first  carried  on  by  separate 
tests:  this  method,  originated  in  Germany,  has  been 
very  extensively  employed  and  further  developed  in 
France  and  especially  in  America.  Then  arose  in 
France  Binet's  system  of  tests  ivith  age  gradations 
that  we  have  already  mentioned.  England  has 
lately  joined  the  movement  to  good  effect  by  giving 
us  the  correlation  method  for  use  in  the  more  pre- 
cise testing  of  intelligence  (Pearson,  Spearman, 
et  al.)  These  three  main  lines  of  activity  will  fur- 
nish the  principle  of  division  of  our  subsequent  treat- 
ment. 

(d)  Normal  adults.  Here  we  find  ourselves  in 
a  realm  whose  exploitation  is  entirely  in  the  future, 
for  the  tests  of  intelligence  thus  far  administered  to 
normal  adults  have  not  been  undertaken  for  the 
sake  of  these  persons,  but  only  to  get  comparative 
standards  for  abnormal  persons.  Yet  even  now  new 
developments  are  to  be  noted.  Miinsterberg  shows 
how  important  an  exact  knowledge  of  individuality 
would  be  for  determining  choice  of  a  vocation  and 
he  has  already  suggested  ways  in  which  the  voca- 


NATURE  AND  PROBLEM   OF  INTELLIGENCE  TESTING        11 

tional  bureaus  that  exist  in  America  might  arrange 
psychological  tests  (19,  20).  And  Captain  Meyer 
(17,  18)  sees  in  intelligence  testing  a  method  that 
ought  to  help  the  recruiting  office  to  keep  unfit  can- 
didates off  the  enlistment  rolls. 

These  last  considerations  show  that  the  chief  em- 
phasis of  intelligence  testing,  which  has  hitherto 
lain  wholly  within  psychopathology,  must  in  the 
future  be  shifted  distinctly  toward  normal  psy- 
chology :  so  the  labor  expended  by  psychology  in  se- 
curing a  reliable  method  will  benefit  not  only 
physicians  and  those  concerned  in  teaching  the  ab- 
normal, but  also  jurists,  military  officials,  those  con- 
cerned in  teaching  the  normal  child  and  others. 

But  just  this  anticipated  extension  of  the  practical 
applicability  of  intelligence  tests  necessitates  sev- 
eral words  of  warning. 

(a)  We  are  still  in  the  midst  of  our  preliminary 
work  on  method.    The  methods  that  now  prevail — 
and  this  is  true  also  of  the  Binet-Simon  system — are 
not  yet  to  be  regarded  as  diagnostic  canons  that  ad- 
mit of  official  prescription.    The  law  passed  in  New 
Jersey  that  directs  the  use  of  intelligence  tests  with 
all  pupils  suspected  of  backwardness  seems  on  this 
account  very  premature.     So,  too,  it  will  be  long, 
very  long,  before  we  realize  the  optimistic  hope  that 
Spearman  attaches  to  the  correlation  method  of  test- 
ing intelligence,  when  he  says:  " Indeed,  it  seems 
possible  to  foresee  the  day  when  there  will  be  an  an- 
nual official  determination  of  the  ' intellectual  index' 
of  every  child  in  the  empire"  (Hart-Spearman;  75, 
p.  78).  " 

(b)  It  must  be  understood  that  tests  of  intelli- 


12     PSYCHOLOGICAL    METHODS   OP   TESTING   INTELLIGENCE 

gence  are  not  easy  to  conduct.  Their  administra- 
tion demands  extended  practise,  psychological  train- 
ing, and  a  critical  mind.  Thus,  for  instance,  the 
average  teacher,  whose  work  has  been  with  the 
wholly  different  methods  of  pedagogical  question- 
ing and  examining,  is  very  apt  to  apply  psychologi- 
cal tests  in  those  forms  in  which  their  value  would 
be  positively  illusory.  If,  accordingly,  the  use  of 
tests  for  practical  purposes  shall  attain  any  very 
large  currency,  the  training  of  a  specially  psycholog- 
ically drilled  personnel  will  become  a  necessity. 
School  psychologists  would  then  take  their  place  side 
by  side  with  the  school  physicians.6 

What  erroneous  ideas  prevail  concerning  the  ease  of  conducting 
tests  is  illustrated,  e.  g.,  in  the  declaration  of  Captain  Meyer  that 
in  military  enlistment  tests  of  intelligence  could  some  day  be 
carried  on  quite  mechanically  by  subalterns.  But,  as  a  matter  of 
fact,  a  psychological  test  is  quite  a  different  thing  than  the  de- 
termination of  weight  or  of  stature  which  might  very  well  be 
carried  out  by  minor  military  officers. 

(c)  Psychological  tests  must  not  be  overesti- 
mated, as  if  they  were  complete  and  automatically 
operative  measures  of  mind.  At  most  they  are  the 
psychographic  minimum  that  gives  us  a  first  orien- 
tation concerning  individuals  about  whom  nothing 
else  is  known,  and  they  are  of  service  to  complement 
and  to  render  comparable  and  objectively  grad- 
able  other  observations — psychological,  pedagogical, 
medical — not  to  replace  these.7 

'Similar  warnings  against  the  oVerestimation,  mechanization 
and  diletante  employment  of  tests  are  to  be  found  in  Myers  (21), 
Bobertag  (40),  and  also  in  Binet's  last  work  (37,  pp.  155  ff.). 

[Cf.  also  the  translator's  Manual  of  Mental  and  Physical  Tests, 
Oh.  1.] 

'On  the  demand  for  school  psychologists,  see  11,  p.  19. 

[The  situation  in  America  is  discussed  by  J.  E.  W.  Wallin  in 
two  interesting  papers,  Jour,  of  Educ.  Psychol.  2:  1911,  121  and 
191. — Translator.} 


I.    Single  Tests  and  Series  of  Tests 

1.    Single  Tests 

All  psychological  experiments  may  be  divided,  ac- 
cording to  their  problem,  into  research  experiments 
and  test  experiments.  The  latter  are  now  generally 
known  as  "tests;"  their  aim  is  "to  determine  for  a 
given  individual  his  mental  constitution  or  person- 
ality or  to  determine  a  single  one  of  his  mental 
traits.1'^  Tests  include,  of  course,  not  only  experi- 
ments in  the  narrower  meaning  of  an  investigation 
carried  out  with  the  aid  of  instruments,  but  also 
simple  methods  of  procedure  that  do  not  involve  the 
use  of  instruments — questions,  problems,  presenta- 
tion of  pictures,  and  the  like — provided  that  these 
are  administered  in  a  systematic  and  scientifically 
regulated  manner  and  that  their  results  are  re- 
corded. 

Now,  in  no  field  have  so  many  tests  been  proposed 
and  put  into  operation  as  in  the  field  of  intelligence 
testing.  To  give  a  complete  exposition  of  all  these 
test  methods  and  of  the  results  that  have  been  gained 
through  them  would  exceed  the  bounds  of  this 
monograph.  But  this  is  not  necessary,  after  all,  be- 
cause, as  will  be  shown  in  a  moment,  the  funda- 
mental significance  of  our  whole  problem  lies  not  in 

JSee  my  earlier  text  (1,  p.  87). 

13 


14     PSYCHOLOGICAL    METHODS   OP   TESTING    INTELLIGENCE 

the  single  tests,  but  in  the  construction  of  well-con- 
sidered systems  of  tests,  for  which  single  tests 
merely  supply  the  raw  material.  So  we  shall  con- 
tent ourselves  in  this  part  of  our  essay  with  a  cur- 
sory survey  without  any  pretense  at  all  to  complete- 
ness.2 

The  varied  nature  of  the  proposals  and  test  inves- 
tigations thus  far  made  is  due  to  the  fact  that  the 
same  problem  has  been  approached  in  very  different 
ways. 

(a)  For  a  long  time  we  started  from  the  errone- 
ous presupposition  that  any  psychological  method  of 
experimentation  would  be  really  usable  as  a  test. 
It  was  thought  that  all  that  was  necessary  was  to 
alter  the  direction,  so  to  speak,  of  the  plan  of  in- 
vestigation. When  a  large  number  of  measurements 
had  been  secured  by  a  single  method  on  a  few  per- 
sons in  the  laboratory,  the  same  method  was  ap- 
plied to  many  persons,  but  only  once  or  a  few  times 
to  each  of  them.  If  it  turned  out  from  such  a  mass 
experiment  that  the  more  intelligent  persons  ob- 
tained, all  things  considered,  better  average  scores 

"For  all  the  literature  on  single  tests,  see  my  text  on  differential 
psychology  (1,  426  ff. )  ;  also  in  Appendix  II  of  that  book  there  is  a 
survey  of  the  relation  of  the  single  tests  to  school  performance. 
Fifty-four  different  tests,  with  numerous  sub-types  are  described, 
together  with  their  methods  and  chief  results,  in  Whipple's 
Manual  (28).  A  very  large  collection  of  materials  for  testing  was 
exhibited  by  the  Institute  for  Applied  Psychology  at  the  Berlin 
Congress,  Easter,  1912,  for  information  about  which  Lipmann's 
catalog  in  the  report  of  the  Congress  may  be  consulted.  Since 
the  meeting,  this  exhibit  has  been  made  a  permanent  one  and  has 
been  assigned  a  room  in  the  exhibition  by  the  Prussian  Ministry  of 
Education  of  German  material  for  instruction,  at  Berlin,  126 
Friedrichstrasse.  The  exhibit  can  be  seen  at  that  place  by  pre- 
vious appointment  with  the  Secretary  of  the  Institute  (Dr.  Lip- 
mann,  Telephone  Potsdam,  No.  8). 


SINGLE  TESTS  AND  SERIES  OF  TESTS          15 

than  the  less  intelligent,  then  it  was  assumed  that 
the  method  would  answer  for  testing  intelligence. 

Nearly  all  the  methods  that  were  familiar  to  the 
psychological  experimenter  have  been  tested  out  in 
this  way,  especially  in  the  earlier  periods  of  in- 
vestigation by  mental  tests,  e.  g.,  measurements  of 
reaction-time,  determinations  of  the  threshold  of 
differential  sensitivity  in  the  different  modalities, 
optical  illusions,  experiments  on  motor  skill  or 
strength,  association  experiments,  tachistoscopic  ex- 
periments, learning  of  syllables,  etc.  In  some  cases, 
it  is  true,  numerous  results  of  interest  were  secured, 
but  it  must  be  admitted  that  a  good  deal  of  energy 
has  been  expended  to  little  avail  in  these  experi- 
ments. 

(b)  A  significant  advance  was  made  when  it  was 
finally  recognized  that  this  blind  probing  about 
could  not  lead  us  farther,  that,  on  the  contrary,  tests 
of  intelligence  must  be  definitely  selected  on  the 
basis  of  certain  presuppositions  that  were  to  be 
made  concerning  the  nature  of  intelligence.  Investi- 
gators, therefore,  sought  then  for  exact  methods  of 
experimentation  that  would  bring  intelligence  into 
direct  and  manifest  operation.  To  be  sure,  the  prob- 
lem was  at  first  conceived  of  in  a  still  too  simple 
form,  in  that  intelligence  was  thought  to  be  exhibited 
as  a  definite  clean-cut  mental  phenomenon  and  the 
plan  of  testing  was  directed  to  the  examination  of 
this  assumed  special  phenomenon. 

The  best-known  instance  of  this  is  the  so-called 
'combination  method'  of  Ebbinghaus,  now  better 
designated  as  the  'completion  method'  (5).  In  Eb- 
binghaus' view,  every  true  instance  of  intellectual 


16     PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

ability  may  be  reduced  in  the  last  analysis  to  an  act 
of  ' combining'  i.  e.,  to  a  process  of  synthetizing  con- 
scious contents  that  previously  had  been  present 
separately ;  accordingly,  he  invented  that  method  in 
which  the  subject  of  the  test  is  to  supply  the  correct 
connections  between  the  separated  parts  of  a  text  in 
which  gaps  have  been  introduced. 

This  principle  of  combination  or  completion  has 
been  used  by  many  other  investigators  as  a  basis 
for  various  forms  of  test. 

Thus,  Ries  (78)  used  two  tests  to  measure  the  ability  to  bring 
two  terms  into  a  logical  relation :  A :  Pairs  of  words  were  pre- 
sented that  had  a  logical  connection,  e.  g.,  fire-smoke,  flood-need; 
then  a  test  was  made  whether  the  naming  of  the  first  member  of 
the  pair  reinstated  the  second  by  dint  of  the  logical  connection. 
B.  Single  words  were  given  to  which  such  words  were  to  be  ad- 
joined as  would  form  a  causally  connected  pair.  A  similar  method 
is  that  of  Winteler  in  which  a  term  is  to  be  named  that  is  super- 
ordinate,  sub-ordinate  or  co-ordinate  to  the  word  given. 

The  combination  test  of  Masselon  in  which  a  meaningful  sen- 
tence is  to  be  made  from  three  given  words  has  been  extensively 
used.  Recently,  Meumann  (16)  has  elaborated  this  method  in  a 
special  fashion ;  he  presents  words  so  chosen  that  they  can  be 
joined  in  a  sentence  either  in  a  banal  and  logically  rather  crude 
way  or  in  a  logically  pertinent  way,  e.  g.,  ass,  Mows;  poor  solution 
"The  ass  receives  blows."  Good  solution  "The  lazy  ass  receives 
blows."  The  tendency  toward  the  former  or  the  latter  rendition 
is  taken  as  an  index  of  intelligence. 

Heilbronner's  picture-test  (8,  27)  examines  ability  to  complete 
in  the  sphere  of  vision :  the  outline  of  an  object  is  shown  on  a 
series  of  small  cards  and  in  such  a  way  that  there  is  a  pro- 
gressive development  from  an  initial  very  fragmentary  outline  by 
successively  more  detailed  stages  up  to  a  complete  picture  of  the 
object.  The  idea  is  to  find  out  at  what  stage  of  incomplete  delinea- 
tion the  object  can  be  recognized. 

To  this  class  of  tests  belongs  also  the  fitting  together  of  cut  up 
pictures  (method  of  the  Russian  alienists,  Bernstein  and  Rosso- 
limo). 

Other  psychologists,  however,  have  considered 
other  and  quite  different  mental  functions  to  be  the 
touch-stone  of  intelligence. 


SINGLE  TESTS  AND  SERIES  OP  TESTS          17 

Thus,  in  an  earlier  stage  of  his  work  Binet  (2)  be- 
lieved that  the  essence  of  intelligence  was  capacity 
to  adjust  attention :  for  this  reason  he  used  tests  of 
attention,  like  the  cancellation  of  letters  in  a  speci- 
fied text  (the  Bourdon  test),  the  copying  of  sentences, 
the  esthesiometer  (Binet  regarded  the  discrimina- 
tion of  two  near-lying  compass-points  as  a  phenom- 
enon of  attention,  not  of  sensation),  the  sorting 
of  cards  containing  the  alphabet,  or  numbers,  etc. 
In  the  work  of  Meumann  (14)  we  note  at  times  the 
laying  of  a  certain  one-sided  emphasis  on  the  under- 
standing of  the  abstract  as  being  the  root  of  intelli- 
gence. This  was  why  he  specially  recommended  the 
use  in  testing  of  the  retention  of  abstract  words. 
Quite  a  number  of  investigators  have  directed  their 
attention  particularly  to  capacity  to  apprehend  as 
the  index  of  intelligence,  and  hence  have  preferred 
to  use  for  tests  such  things  as  the  apprehension  of 
pictures  or  ability  to  perceive  linguistic  material  of 
different  contents  and  extents. 

(c)  We  may  consider  as  a  third  main  class  of 
tests  those  patterned  after  familiar  pedagogical 
tasks.  There  are,  indeed,  certain  school  activities 
that  admit  of  relatively  precise  grading,  since  they 
can  be  rated  both  in  terms  of  quantity  (amount  done 
within  a  given  time)  and  in  terms  of  quality  (fre- 
quency of  mistakes).  Those  schoolroom  tasks  are 
most  obviously  adaptable  for  psychological  pur- 
poses within  which  the  course  of  activity  is  fairly 
homogeneous,  e.  g.,  the  computation  of  specified 
arithmetical  problems,  writing  from  dictation,  com- 
mitting to  memory  of  vocabularies  and  poems,  and 
all  these  tasks  have,  in  fact,  been  used  for  testing  in- 


18     PSYCHOLOGICAL   METHODS  OB'   TESTING   INTELLIGENCE 

telligence.  Evidently  a  chief  objection  to  this 
method  is  that  the  activities  mentioned  are  depen- 
dent to  a  large  degree  upon  external  conditions  of 
the  instruction,  so  that  the  intelligence  of  individ- 
uals that  are  working,  or  that  have  worked,  under 
different  school  conditions  cannot  be  subjected  to 
comparative  tests  by  means  of  these  activities. 

(d)  A  fourth  main  class  of  tests  is  still  farther 
removed  from  the  precision  of  the  laboratory  ex- 
periment, but  is  thereby  more  nearly  allied  to  real 
life.  These  tests  aim  to  secure  records  of  such  evi- 
dences of  intelligence  as  are  accepted  in  ordinary 
life  as  special  evidence  of  it.  These  direct  tests  of 
intellect  have  been  specially  developed  by  the  psy- 
chiatrists: they  comprise  such  things  as  defining, 
comparing,  differentiating,  the  understanding  of 
proverbs,  grasping  the  point  of  a  joke,  seeing  ab- 
surdities in  verbal  or  pictorial  presentations. 

These  tests  have  the  advantage  that  in  them  in- 
telligence is  undoubtedly  much  more  directly  opera- 
tive than  in  the  others :  but  on  this  account  it  is  im- 
possible in  most  of  them  to  scale  the  results :  they 
are  '  *  alternative  tests, ' '  that  admit  of  but  the  rough 
differentiation  into  right  or  wrong  (+  or  — ).  The 
single  test  of  this  sort,  therefore,  does  not  make  it 
possible  to  secure  any  very  precise  characterization 
of  the  person  tested,  or  to  rank  him  in  a  scale. 

2.     The  Inadequacy  of  the  Single  Test 

A  critique  of  all  these  confusingly  many  attempts 
might  be  undertaken  by  examining  them,  test  by  test, 
to  see  which  ones  deserve  to  be  recommended  as  in- 
dicators of  intelligence.  But  we  feel  that  far  more 


SINGLE  TESTS  AND  SERIES  OF  TESTS          19 

important  than  such  a  special  scrutiny  of  single  tests 
is  the  laying  of  emphasis  upon  a  general  critical 
position :  no  single  test,  no  matter  how  good  it  may 
be,  should  ever  be  made  the  instrument  for  testing 
the  intelligence  of  an  individual* 

Because  the  single  test  tests  on  the  one  hand  more, 
and  on  the  other  hand,  less  than  it  really  ought  to 
test. 

More,  because  the  mental  activity  that  is  aroused 
in  a  subject  by  an  experimental  task,  a  test-question, 
or  the  like,  is  the  fused  resultant  of  quite  varied  an- 
tecedent conditioning  factors:  and  we  do  not  know 
what  share  that  particular  conditioning  factor  that 
we  call  intelligence  played  in  the  performance.  In 
this  equivocal  nature  of  the  object  under  investiga- 
tion lies  the  too  often  little  noted  distinction  between 
tests  and  laboratory  experiments.  If  I  arrange  an 
investigation  of  memory  in  the  laboratory,  I  know 
that  I  am  actually  examining  memory  and  not  some- 
thing else,  because  in  numerous  single  experiments 
I  vary  in  a  measurable  way  certain  conditions  only 
of  the  function  of  memory  while  I  keep  all  the  other 
conditions  constant.  &ut  when,  on  the  contrary,  I 
administer  a  test  of  learning  or  a  test  of  immediate 
memory  by  itself  to  a  person,  the  outcome  is  affected 
by  the  real  capacity  of  retention,  understanding  of 
the  material,  attention,  interest,  etc.,  all  without  con- 
trol— and  this  quite  regardless  of  the  disposition 
of  the  subject  at  the  time.  Or,  take  another  exam- 


•Cf.  Binet  (36,  p.  201)  :  "One  test  has  no  meaning,  but  five  or 
six  tests  do  mean  something.  *  *  *  The  attention  of  psy- 
chologists must,  then,  be  called  especially  to  this  principle  of  the 
multiplicity  of  tests." 


20     PSYCHOLOGICAL    METHODS   OF   TESTING   INTELLIGENCE 

pie :  suppose  that  a  subject  has  made  a  good  record 
in  the  filling  out  of  gaps  in  a  text  (Ebbinghaus'  com- 
pletion test),  does  this  good  performance  depend 
predominantly  upon  a  real  capacity  for  logical  com- 
bination? Or  upon  a  specially  large  vocabulary? 
Or  upon  a  fine  feeling  for  language?  Or  upon  prac- 
tise in  guessing  riddles  ? 

The  only  way  to  analyze  out  from  this  fused  re- 
sultant the  ability  we  are  after — in  this  case,  for  in- 
stance, the  ability  to  effect  combinations — is  obviously 
to  add  several  more  tests  of  a  different  kind  that 
will  also  involve  the  process  of  combining,  but  that 
will  in  addition  involve  mental  processes  of  quite 
different  sorts.  Correspondences  that  may  appear 
in  the  results  of  these  different  tests  may  then  be 
ascribed  with  probability  to  their  common  factor — 
in  our  example,  to  the  ability  to  effect  combinations. 
The  ability  sought  for  must,  therefore,  be  plotted, 
as  it  were,  from  different  positions. 

Too  little.  But  suppose  that  we  have  succeeded 
in  determining  a  subject's  ability  to  make  combina- 
tions not  by  a  single  test  but  by  a  smaller  number  of 
different  'combination'  tests,  have  we  then  meas- 
ured his  intelligence?  By  no  means,  for  we  have 
now  determined  far  too  little.  Intelligence,  it  is  to 
be  noted,  means  an  all-round  ability ;  it  refers  to 
the  general  mental  attitude  toward  new  demands, 
and  combining  is  only  one  side  of  this  attitude.  The 
other  sides  possess  equal  significance,  e.  g.,  the 
grasping  by  consciousness  of  a  newly  presented  ob- 
ject (apprehension,  apperception,  understanding), 
the  dividing  of  a  whole  into  its  parts  (analysis),  the 
taking  of  an  intellectual  attitude  toward  a  content 


SINGLE   TESTS  AND   SERIES  OF   TESTS  21 

(judging,  criticizing,  deliberating,  and  deciding), 
etc. 

These  functions  of  intelligence  must,  then,  be  con- 
sidered in  their  totality;  and  the  actual  testing  of 
them  ought  not  to  be  omitted  unless  we  were  certain 
that  they  had  already  been  examined  by  implication 
along  with  some  other  tested  function.  Suppose 
that  in  a  group  of  persons  it  had  been  possible  to 
show  that  X  had  the  best  ability  to  combine;  is  it 
then  certain  that  he  would  also  take  first  place  in 
other  forms  of  activity  involving  intelligence  and 
that  he  might,  accordingly,  be  ranked  first  in  total 
intelligence? 

To  ask  this  question  is  enough  to  insure  a  nega- 
tive reply.  I  feel,  I  admit,  that  Spearman  (75,  77, 
80)  is  right  in  asserting  that  intelligence  does  really 
signify  a  general  capacity  which  colors  in  a  definite 
way  the  whole  mental  behavior  of  an  individual. 
But  we  must  not  force  this  idea — nor  does  Spear- 
man— so  far  as  to  assume  that  all  the  separate  con- 
stituent functions  of  intelligence  in  the  different 
fields  are  mechanically  of  equivalent  degree.  Such 
a  view  is,  indeed,  contradicted  by  the  circumstance 
that  there  is  operative  in  each  individual  bit  of  be- 
havior not  only  a  given  quantity  of  intelligence,  but 
also  the  special  quality  of  intelligence  of  the  person 
tested,  and  besides  these  a  varied  number  of  other 
mental  traits.  Thus,  there  are  persons  who  have  a 
pretty  high  grade  of  general  intelligence,  but  who 
manifest  it  much  better  in  analytic  and  critical  than 
in  synthetic  work ;  again,  there  are  persons  in  whom 
the  receptive  activities  of  intelligence  (apprehend- 
ing and  understanding)  are  superior  to  the  more 
spontaneous  activities,  and  so  on. 


22     PSYCHOLOGICAL   METHODS   OP   TESTING   INTELLIGENCE 

However,  everyday  life  shows  that  we  can  disre- 
gard these  qualitative  differences  and  nevertheless 
may  characterize  the  general  grade  of  intelligence 
that  a  man  possesses.  When  we  do  this  we  make, 
even  unconsciously,  certain  compensations :  two  per- 
sons may  have  an  intelligence  of  the  same  value,  but 
of  somewhat  different  kinds.  In_  tests  there  must  be 
introduced  a  kind  of  systematic  compensation  like 
this.  We  must  test  the  different  phases  of  the  activ- 
ity of  intelligence  and  seek  to  construct  a  general 
picture  of  the  degree  of  intelligence  from  the  differ- 
ent results,  partially  accordant,  partially  variant  as 
they  will  be. 

This  has  given  us  a  clear  idea  of  what  is  wanted 
in  the  methodics  of  intelligence  testing. 

Negatively,  it  must  be  declared  that  the  method 
of  isolated  tests,  the  idea  of  basing  everything  on  a 
single  test,  is  methodologically  no  better  than  such  a 
procedure  as  judging  the  total  character  of  a  man 
on  the  strength  of  the  single  arbitrarily  selected 
symptom  of  his  handwriting  (graphology). 

Positively,  three  things  are  evident:  first,  series 
of  tests  must  be  arranged  that  will  set  in  play  the 
various  constituent  functions  of  intelligence;  sec- 
ondly, for  this  purpose  there  must  be  a  wise  selec- 
tion of  tests ;  out  of  the  immense  number  of  possible 
tests  only  those  should  be  chosen  that  afford  a  de- 
cided and  a  reliable  symptomatic  value,  general  ap- 
plicability, and  possibility  of  objective  evaluation; 
thirdly,  there  must  be  created  a  system  by  means  of 
which  the  several  particular  results  of  the  testing 
can  be  united  into  one  resultant  value,  i.  e.,  a  value 
that  shows  the  grade  of  intelligence  of  the  subject 
objectively  in  an  inclusive  formula  in  which  per- 


SINGLE   TESTS  AND   SERIES  OF   TESTS  23 

f  ormances  of  different  degrees  of  value  shall  in  some 
way  be  compensated. 

3.    Series  of  Tests 

The  first  of  these  positive  requirements  has  al- 
ready been  met  for  a  long  time  since;  in  especial, 
since  Eieger  numerous  test  series  have  been  used  by 
the  psychiatrists  for  testing  intelligence.  These 
series  have  been  based  as  a  rule  upon  a  psycholog- 
ical schema,  though  this  schema  has  varied  a  good 
deal  from  one  investigator  to  another.  For  illus- 
tration two  such  series  may  be  mentioned,  both  of 
them  quite  recent. 

Soininer  (26),  in  an  article  just  published  on  the  methods  of 
intelligence  testing,  discusses  in  order  the  materials  for  testing 
the  following  aspects  of  the  problem :  relation  of  memory,  of 
school  information,  of  arithmetical  ability  and  of  association  to 
understanding,  also  attention,  capacity  to  apprehend,  completeness 
of  complexes,  analysis  of  complexes,  redintegration  of  complexes, 
mechanical  knowledge  (cleverness),  constructive  knowledge,  logi- 
cal subordination  and  superordination,  notion  of  cause  and  effect, 
intellectual  interests,  understanding  of  the  environment. 

Ziehen  (30),  in  the  last  (3d)  edition  of  his  Prinzipien  und  Mcth- 
oden  der  Intelligenzpriifung,  makes  the  following  classification : 
retention,  development  and  differentiation  of  ideas  (generalization, 
isolation  and  complexion  of  ideas),  reproduction  and  combination, 
and  describes  the  numerous  forms  of  questions  and  tests  used  in 
his  clinic  for  each  of  these  divisions. 

Although  one  cannot  deny  that  these  and  other 
series  devised  by  psychiatrists  are  quite  compre- 
hensive, yet  they  are  open  to  criticism  in  other  re- 
spects :  the  requirements  that  were  laid  down  above, 
under  6  and  c,  are  met  by  them  only  partially  or  not 
at  all.  For  all  these  series  give  the  impression  that 
the  selection  of  tests  may  have  been  more  a  matter 
of  chance  or  arbitrary  choice  than  something  deter- 
mined by  actual  guaging  of  their  value.  As  a  rule 


24     PSYCHOLOGICAL    METHODS   OF   TESTING   INTELLIGENCE 

the  selection  was  based  upon  a  priori  reasoning  that 
a  certain  capacity,  e.  g.,  retention  or  combination, 
which  had  been  assumed  to  belong  to  intelligence 
was  l  hit '  by  a  certain  kind  of  test.  Very  seldom  was 
any  actual  preliminary  investigation  made  to  see 
whether  this  particular  test  was  really  superior  to 
so  and  so  many  others  by  virtue  of  the  precision, 
constancy  and  significance  of  the  particular  values 
that  it  afforded.  Moreover,  this  chance  selection  evi- 
dently explains  why  there  is  so  little  agreement  be- 
tween the  test  series  of  different  investigators: 
every  psychiatrical  clinic  has  its  own  special  method 
of  testing  intelligence;  every  specialist  in  nervous 
diseases,  every  physician  in  charge  of  classes  for 
subnormals  chooses  his  tests  to  suit  his  fancy,  and 
thus  it  has  been  impossible,  so  far,  to  effect  any  real 
comparison,  corroboration  and  standardization  of 
the  results  of  different  investigators. 

Finally,  the  usual  psychiatrical  test-series  suffer 
from  the  lack  of  any  principle  by  which  to  summar- 
ize the  results  in  a  single  value.  The  psychiatrists 
recognize  that  it  is  impossible  to  set  a  value  on  the 
intelligence  of  a  person  as  a  whole,  for  they  apply 
such  predicates  as  "poor  in  judgment,"  "mentally 
feeble,"  "imbecile,"  "idiotic;"  but  if  we  watch  the 
way  in  which,  in  the  individual  case,  they  arrive  at 
the  general  conclusion  that  they  draw  from  the  data 
of  their  test-series,  we  note  a  yawning  gap*'  The 
mosaic  of  test  results  is,  and  remains,  only  raw  ma- 
terial ;  no  fundamental  methodological  principle,  but 
only  intuition,  routine  and  subjective  estimation  of 
their  results,  dictates  the  final  decision  concerning 
the  intelligence  of  the  subject.  In  a  certain  sense, 


SINGLE   TESTS  AND   SERIES  OF   TESTS  25 

there  is  an  advantage  in  deciding  in  this  way,  for  the 
gift  —  wellnigh  an  artistic  gift  —  of  intuitive  appre- 
ciation and  sympathetic  understanding  is  peculiarly 
indispensable  to  the  psychiatrist.  But  if  we  leave 
H  m\\  "T  n"""mit;  there  remains  a 


decided  disadvantage,  because  every  conclusion  ar- 
rived at  by  this  method  then  remains  a  subjective 
one  that  cannot  be  controlled  or  subjected  to  gener- 

talization.  On  this  account  we  are  justified  in  de- 
manding that,  at  least  in  addition  to  this  intuitive 
diagnosis,  there  should  also  be  a  method  for  making 
an  objective  evaluation  of  the  results.  To  meet  this 
demand  these  mere  collocations  of  tests  will  have  to 
be  replaced  by  a  closed  system  of  tests  which  will 
permit  the  derivation  of  a  final  general  index  of  in- 
telligence from  the  results  obtained  from  any  subject 
whomsoever,  and  that  in  accordance  with  prescribed 
rules  that  can  be  applied  in  a  comparable  way  in  all 
places  and  on  men  of  different  grades  of  intelligence. 

An  alienist  has  come  forward  lately  with  an  attempt  of  this  sort, 

i.  e.,  an  attempt  to  join  together  a  series  of  tests  systematically  so 

as  to  furnish  a  'picture'  of  an  individuality.     I  refer  to  the  so- 

called    'profile-method'    of   the    Russian,    Rossolimo    (23-24a)  :    a 

^^-method  that  really  includes  more  than  mere  tests  of  intelligence 

^.        and  comes,  therefore,  but  partially  within  our  scope. 

Rossolimo  has  contrived  ten  tests  for  each  of  ten  different  men- 
tal functions.  The  results  obtained  from  the  single  subject  are 
set  out  graphically  by  erecting  ordiuates  corresponding  to  the 
number  of  the  tests  achieved  for  each  of  the  functions  under  test. 
The  ends  of  these  ordinates  are  then  joined  to  make  a  curve  that 
Rossolimo  calls  the  'individual  profile.'  This  profile  line  is  sup- 
posed to  furnish  a  pictorial  representation  of  the  total  nature  of 
a  patient.  Thus,  for  instance,  in  those  disorders  in  which  the  ca- 
pacity of  immediate  reproduction  is  decidedly  reduced  while  the 
other  capacities  remain  unaffected,  the  profile  will  show  a  sharp 
notch  at  a  definite  point,  and  so  on. 

The  tests  proposed  by  Rossolimo  have  many  commendable  feat- 
ures; we  may  note,  for  example,  the  little  puzzles,  like  the  sepa- 
rating of  two  interlaced  wire  nooses,  etc.,  that  are  used  to  test 


26     PSYCHOLOGICAL    METHODS   OF   TESTING   INTELLIGENCE 

technical  ability.  Yet,  on  the  whole,  the  principle  of  the  con- 
struction of  the  profile  is  too  superficial  and  the  coordination  of 
certain  tests  to  certain  mental  functions,  e,  g.,  to  volitional  acts, 
is  not  precise  enough  to  alloAA*  us  to  hope  for  much  success. 

This  demand  for  a  system  of  tests  presents  such 
an  exceedingly  difficult  scientific  problem  that  it  is 
perfectly  evident  that  alienists  and  educators  can 
not  solve  it  as  a  side  issue  of  their  professional  work, 
but  that  psychology  itself  will  have  to  undertake  the 
task.  It  is  interesting  in  this  connection  to  note  how 
psychology  attacked  the  problem  along  two  very  dif- 
ferent lines.  I  feel  that  it  is  important  to  consider 
them  separately  in  what  follows.  Neither  of  these 
two  lines  of  effort  should  be  regarded  as  the  only 
correct  one ;  each  method  has  its  advantages  and  its 
disadvantages,  and,  what  is  particularly  important, 
each  has  its  special  aim  for  which  it  is  fitted.  The 
method  of  age-gradation  of  Binet  and  Simon  permits 
of  a  rough  gradation  of  intelligence  for  the  whole 
range  of  development  of  the  child ;  it  is  for  use  in  a 
comparable  manner  with  children  of  different  ages, 
of  different  nationality  and  cultural  level,  with 
normal  and  with  feeble-minded  children  of  all 
grades.  The  method  of  rank  correlation,  on  the 
other  hand,  is  limited  thus  far  to  a  comparison  of  the 
members  of  a  small  homogeneous  group,  but  renders 
it  possible  to  test  the  gradation  of  intelligence  with- 
in this  group  with  a  precision  that  the  Binet  method 
can  not  approximate.  A  considerable  amount  of  ma- 
terial is  already  available  for  the  first  of  these 
methods,  and  we  shall  have  to  deal  with  it  at  some 
length  for  that  reason.  With  the  second  method,  on 
the  contrary,  our  discussion  will  center  upon  the  out- 
look for  its  future  development. 


SINGLE   TESTS  AND   SERIES  OF  TESTS  27 

Both  methods  have  been  tried  out  so  far  almost 
exclusively  upon  school  children ;  but  it  is  to  be  ex- 
pected that  they  will  find  use  also  in  testing  the  in- 
telligence of  adults,  both  normal  and  mentally  de- 
ficient. 


II.    The  Method  of  Age-Gradation  (Binet-Simon  Method1) 

1.     The  Principle  of  the  Method  and  the  Tests  Em- 
ployed in  It 

In  the  nineties  Binet  and  Simon  conceived  the 
idea  of  constructing  a  "graded  scale  of  intelligence" 
(Echelle  metrique  de  V intelligence)  that  should  be 
especially  planned  for  testing  the  intelligence  of 
children.  The  requirements  to  be  satisfied  by  the 
method  were  the  following.  A  series  of  tests  should 
be  found  for  each  year  of  childhood  the  passing  of 
which  could  be  considered  normal  and  typical  for 
children  of  just  precisely  this  age.  The  tests  must 
be  relatively  uninfluenced  by  external  and  chance 
conditions,  especially  by  school  learning,  so  that  the 
result  might  bring  out  as  purely  as  possible  the  real 
mental  endowment  of  the  child;  they  must  admit  of 
as  uniform  use  as  possible  in  different  nations,  lan- 
guages or  grades  of  culture :  they  should  be  easy  to 
carry  out,  not  necessitate  laboratory  apparatus  or 
instruments  of  precision,  should  not  exact  too  much 


'Comprehensive  descriptions  of  his  method  are  given  by  Binet 
(partly  in  conjunction  with  Simon)  in  references  33  to  37.  A 
general  review  of  the  development  of  the  method  is  given  by 
Bobertag  (39).  [Also  recently  by  Meumann,  Arch.  f.  d.  ge». 
Psych.,  25:  1912  (Literatur,  85  ff.).— Translator.] 

29 


30     PSYCHOLOGICAL    METHODS   OF   TESTING   INTELLIGENCE 

time  of  the  child,  should  not  impose  hardship  on 
him  or  tire  him,  and  yet  must  possess  sufficient  ac- 
curacy to  make  possible  comparison  and  checking  of 
the  investigations  undertaken  by  different  persons; 
and,  finally,  they  should  make  it  possible  to  work  out 
a  final  value  for  each  subject  tested  that  could  be 
deemed  a  measure  of  his  general  intelligence. 

It  seems,  at  first  blush,  as  if  the  fulfilling  of  so 
many  different  demands  would  raise  insurmountable 
difficulties.  Above  all,  there  was  no  preliminary  in- 
formation available  as  to  what  intellectual  perform- 
ance might  be  expected,  even  approximately,  from  a 
child  of  a  given  age.  If  some  time  you  ask  a  teacher 
or  some  one  who  has  been  dealing  with  children  of 
different  ages  for  a  long  time  at  what  age  a  child 
could  be  expected  to  give  correctly  the  difference  be- 
tween two  designated  objects,  e.  g.,  wood  and  glass, 
and  at  what  age  he  would  be  able  to  explain  the  dif- 
ference between  two  abstract  concepts,  e.  g.,  lies  and 
mistakes,  he  would  either  be  silent  or  make  a  blind 
guess  at  it.  Here,  then,  was  virgin  land  to  explore. 
When  to  that  is  added  the  conditions  that  have  just 
been  stated,  many  of  which  are  hard  to  reconcile 
with  one  another — freedom  from  school  training, 
general  ease  of  application,  brevity,  precision,  possi- 
bility of  quantitative  evaluation,  there  can  be  no 
doubt  that  there  was  laid  down  here  one  of  the  hard- 
est problems  that  applied  psychology  had  set  for 
itself  up  to  this  time. 

Nevertheless,  the  difficulty  has,  in  principle,  been 
overcome.  Of  course  this  does  not  mean  that  the 
present  form  of  the  method  can  be  regarded  as  a 
final  form :  it  will  doubtless  suffer  so  many  modifica- 


THE   METHOD  OF  AGE  GRADATION  31 

tions  in  the  near  future  that  it  will  hardly  be  recog- 
nized in  the  end.  But  we  know  that  we  are  on  the 
right  track,  and  in  some  future  decades  it  can  be  fully 
appreciated  what  praise  Binet  and  his  co-worker 
Simon  have  deserved  by  directing  us  along  this  path. 

A  short  time  ago — October  18,  1911 — the  gifted 
and  highly  esteemed  creator  of  the  method  died.  His 
all-too-early  demise,  that  we  mourn  most  bitterly, 
compels  others  now  to  pick  up  the  threads  that  he 
had  spun.  At  such  a  moment  it  is  appropriate  to 
summarize  briefly  what  has  been  gained  and  to  point 
out  the  steps  that  are  to  be  taken  for  further  ad- 
vance. 

After  many  years  of  preliminary  empirical  inves- 
tigation to  determine  what  tests  might  be  considered 
normal  for  given  ages,  Binet  and  Simon  published 
(33)  in  the  year  1908,  the  first  complete  account  of 
their  system  or  tests.  It  comprised  a  series  of  from 
five  to  seven  tests  for  each  age  from  three  to  thirteen 
years.  A  revised  draft  appeared  in  1911  (35,  36)  in 
which  many  tests  are  modified,  many  shifted  to  dif- 
ferent age-years  and  the  number  of  tests  for  each 
age-grade  brought  uniformly  to  five.  The  1911  sys- 
tem replaces  tests  for  11,  12  and  13-year-olds  by 
tests  for  13  and  15-year-olds  and  adults. 

A  list  of  all  the  investigations  conducted  on  the 
B.  S.  tests  to  date  is  given  in  the  bibliography  at  the 
end.  In  the  appendix  there  are  brought  together  in 
comparative  form  the  series  of  tests  proposed  for 
each  age  by  Binet  and  Simon  in  1908,  and  1911,  by 
Bobertag,  and  by  Terinan  and  Childs. 

As  a  glance  at  the  list  of  tests  shows,  almost  all  of 
them  are  of  the  alternative  type,  i.  e.,  they  are  tests 


32     PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

in  which  performance  can  not  be  graduated,  but  can 
only  be  scored  right  or  wrong  (-}-  or  — ).  Failure 
to  reply  at  all  is  counted  'minus'  just  as  much  as  an 
expressly  given  wrong  answer.  It  must  be  admitted 
also  that  it  is  often  quite  hard  to  decide  in  a  given 
case  whether  to  rate  an  answer  +  or  — :  the  only 
way  to  do  this  with  certainty  is  to  practise  for  a 
long  time  and  to  observe  uniformly  the  criteria  that 
have  been  chosen  for  the  decision. 

The  tests  are  extremely  varied  in  nature. 

Memory  is  tested,  on  the  one  hand  as  immediate  memory  for 
digits  and  sentences  of  different  lengths,  for  a  story  that  is  read, 
and  for  three  simple  orders  given  together,  and  on  the  other  hand 
as  possession  of  simple  everyday  knowledge  (days  of  the  week, 
months,  coins,  right  and  left).  Size  and  availability  of  vocabulary 
is  determined  by  the  number  of  words  that  can  be  named  in  three 
minutes. 

Since  1911  a  test  of  suggestibility  (judgment  of  line-lengths) 
has  been  introduced. 

Motor  abilities  are  tested  by  some  tests  of  drawing  from  copy, 
paper  cutting  and  writing.  Practical  accomplishments  are  in- 
volved in  counting  coins,  making  change  for  a  larger  coin,  exe- 
cuting the  three  commissions  just  mentioned. 

Mbst  of  the  tests,  however,  aim  more  directly  at  intellectual 
activities.  Comparison  and  discrimination  are  dealt  with  in  va- 
rious forms,  e.  g.,  sensory  comparison  (of  small  boxes  of  like  ap- 
pearance, but  unlike  weight),  logical  discrimination  from  memory, 
both  between  concrete  terms  (wood  and  glass,  fly  and  butterfly) 
and  between  abstract  terms  (lies  and  mistakes)  ;  esthetic  com- 
parison (drawings  of  beautiful  and  ugly  faces).  There  are  also 
tested  defining  of  both  concrete  and  abstract  terms,  the  completing 
of  omissions  in  a  text,  the  combining  of  three  words  into  a  sen- 
tence, orderly  arranging  both  of  sensory  material  (putting  five 
little  boxes  in  order  according  to  their  weight),  and  of  logical, 
verbal  material  (placing  jumbled-up  words  in  a  sentence)  ;  the 
intelligent  apprehension  of  a  picture ;  critical  apprehension,  both 
optical  (noting  omissions  in  drawings  of  persons),  and  logical 
(recognizing  inconsistencies  in  certain  sentences)  ;  practical  moral 
intelligence  (by  questions  in  the  form:  'What's  the  thing  to  do 
when  so-and-so  happens?'). 

Many  of  the  tests  recur  in  different  age-levels  in 
such  a  way  that  the  standard  of  performance  de- 


THE   METHOD  OF  AGE  GRADATION  33 

manded  is  varied.  Thus,  the  pictures  are  presented 
to  subjects  of  all  ages ;  enumeration  of  the  pictured 
objects  corresponds  to  the  3-year  old  level,  a  descrip- 
tion of  the  action  that  the  persons  are  carrying  on, 
to  the  7-year  old  level,  a  comprehension  of  the  total 
meaning  of  the  picture  to  the  12-year  old  level.  The 
denning  of  concrete  terms  appears  in  the  6  and  the  9- 
year  stages;  in  the  former,  definition  in  terms  of 
use  suffices,  e.  g.,  ''What  is  a  horse?"  "To  ride;" 
in  the  latter  something  superior  to  this  is  demanded, 
e.  g.,  "What  is  a  horse?"  "An  animal."  Finally, 
the  memory  span  tests  for  digits  and  sentences  are 
graded  into  several  classes  according  to  their  length; 
thus,  after  once  hearing  the  digits,  the  3-year  old 
child  should  be  able  to  repeat  two,  the  4-year  three, 
the  7-year  five,  the  12-year  seven  digits. 

The  individual  tests  are  of  unequal  value.  Many 
are  of  exceptional  merit,  e.  g.,  defining,  describing 
pictures,  answering  questions  that  put  a  premium 
on  intelligence.  It  is  also  a  very  meritorious  feature 
that  there  are  tests  among  them  whose  solution  does 
not  depend  on  readiness  in  the  use  of  speech,  e.  g., 
the  arrangement  of  the  five  weights,  esthetic  com- 
parison, recognizing  omissions  in  pictures:  we  are 
as  a  rule  altogether  too  much  inclined  to  identify 
control  of  verbal  expression  with  intelligence,  an 
inference  that  is  often  false.  Others  of  the  tests, 
however,  are  more  dependent  than  we  could  wish  on 
external,  particularly  on  home  influences,  e.  g.,  know- 
ing coins,  or  are  too  much  mere  functions  of  pure 
mechanical  memory  (reciting  the  days  of  the  week), 
so  that  it  would  be  better  to  supplant  them  by  others 
in  the  future.  It  must  be  recognized  that  any  change 


34     PSYCHOLOGICAL   METHODS  OF   TESTING   INTELLIGENCE 

in  the  selection  and  arrangement  of  these  tests  pre- 
sents a  difficulty  of  quite  another  sort  than  as  if  they 
were  mere  collocations  of  tests:  for,  since  each  of 
these  tests  is  a  factor  in  the  determination  of  the 
final  score,  it  is  possible  that  a  change  may  destroy 
the  equilibrium  of  the  whole  system.  This  is  easy 
to  be  seen  in  the  supplementary  investigation  of 
Binet  and  Simon  themselves,  when  they  tried  to  cor- 
rect their  system  by  the  omission,  insertion  and 
transference  of  particular  tests:  for  trials,  e.  g., 
those  of  Terman  and  Childs  and  of  Chotzen,  have 
shown  that  the  second  edition  (1911)  is  in  many  re- 
spects less  useful  than  the  earlier  form  (1908). 

What  remedies  can  be  devised  for  this  situation 
will  be  discussed  below  (Section  5a). 

The  technique  of  the  Binet-Simon  method  is  by  no 
means  so  easy  as  the  simplicity  of  the  material  used 
would  lead  one  at  first  to  suppose.  It  is  to  be  recom- 
mended that,  so  far  as  is  in  any  way  feasible,  the  ex- 
aminer should  always  do  his  work  with  the  aid  of  an 
assistant  to  keep  the  record,  so  as  to  avoid  the  un- 
desirable division  of  attention  between  testing  and 
recording.  Both  of  these  experimenters  must  have 
gained  a  high  degree  of  practise  and  be  well  used  to 
one  another  before  they  proceed  to  actual  testing. 
The  examiner  must  have  an  almost  mechanical  exact- 
ness and  uniformity  in  the  formulation  of  the  con- 
tinually recurring  questions,  in  the  modulation  of 
his  voice,  etc.,  yet  he  must  be  prepared  for  the  many 
individual  variations  that  appear  in  consequence  of 
different  reactions  of  the  subjects,  and  must  have 
definite  measures  in  readiness  for  use  in  these  junc- 
tures. Never  must  he  permit  it  to  be  seen  that  some 


THE   METHOD  OP  AGE  GRADATION  35 

answers  are  more,  others  less  satisfactory  to  him: 
rather  must  he  maintain  an  attitude  of  uniform  and 
quiet  friendliness.  The  recorder  should  not  confine 
himself  to  the  mere  noting  of  plus  and  minus  signs 
to  show  the  net  outcome  of  each  test,  but  should  also 
note  down  as  fully,  as  possible  what  the  subject  says 
and  also  such  features  of  his  behavior  and  attitude 
toward  the  tests  as  are  worth  noting.  This  is  neces- 
sary both  because  it  is  often  impossible  to  decide 
whether  to  credit  a  test  'plus'  or  'minus'  until  later 
on,  after  quiet  consideration  (and  the  material  must 
be  available  for  that)  and  also  because  it  should 
make  possible  a  qualitative  analysis  of  the  examinee. 
The  individual  subject  ought,  of  course,  to  be 
tested  not  only  with  the  tests  of  his  age,  but  also 
with  a  considerable  part  of  the  whole  series — on  ac- 
count of  the  area  of  scattered  distribution  to  be  dis- 
cussed in  a  moment.  The  examiner  should  begin 
with  tests  that  are  neither  too  easy  nor  too  difficult, 
avoid  monotony  and  introduce  short  pauses  if  fatigue 
becomes  noticeable.  The  testing  of  a  single  indi- 
vidual takes,  for  normals  20  to  30  minutes,  accord- 
ing to  age  and  circumstances,  for  abnormals  from 
one-half  to  three-quarters  of  an  hour,  on  account  of 
the  slower  response. 

In  mass  experiments  there  is  a  source  of  difficulty  in  the  possi- 
bility of  communication  between  those  already  tested  and  those 
to  be  tested.  It  is  true  that  the  danger  of  such  a  'psychic  infec- 
tion' is  not  very  great,  on  account  of  the  peculiar  character  of  the 
material  used  for  the  testing ;  nevertheless,  one  should  avoid,  as 
far  as  may  be,  the  possibility  of  any  spreading  of  information. 
Thus,  for  instance,  it  is  not  advisable  to  test  the  pupils  of  one 
class  on  several  days  in  succession.  If  it  is  desired  to  examine  a 
rather  large  number  of  children  that  belong  in  the  same  group,  the 
plan  followed  at  Breslau  seems  useful:  four  experimenters  (with 
their  clerks),  all  of  whom  had  been  trained  to  conduct  the  tests 


36     PSYCHOLOGICAL   METHODS   OF   TESTING    INTELLIGENCE 

in  the  same  way,  carried  on  tests  the  same  afternoon  in  different 
rooms.  Each  experimenter  could  deal  with  four  or  five  subjects 
in  this  time,  and  each  subject  was  obliged  to  go  home  directly 
after  his  examination ;  in  this  way,  16  to  20  members  of  the  class 
were  tested  without  there  being  possible  any  exchange  of  ideas 
between  them. 

For  all  further  details  of  the  technique  of  these 
tests  the  directions  for  using  them  that  are  already 
available  for  different  nations  must  be  consulted. 

Such  directions  have  been  given  for  the  examina- 
tions of  French  children  by  Binet  and  Simon  in  1911 
(35,  36),  for  English  and  American  children  by 
Whipple  in  his  Manual  (28), by  Wallin  (67)  and  more 
briefly  by  Huey  (9),  and  for  Italians  by  Treves-Saf- 
fiotti  (66).  For  use  in  Germany  Lipmann  first  fol- 
lowed the  original  instructions  as  precisely  as  possi- 
ble, and  then  Bobertag  (40)  described  very  fully  his 
elaboration  of  them  as  based  on  practical  tests— 
an  elaboration  that  differs  from  Binet  and  Simon  to 
advantage  in  some  particulars,  e.  g.,  in  the  choice  of 
pictures.  The  extended  directions  for  testing  and 
questioning  that  Bobertag  has  prepared  should  form 
the  basis  of  all  future  investigations  in  Germany.2 

2.     The  Resultant  Values:  Mental  Age,  Mental  Re- 
tardation, Advance,  and  Arrest;  Mental  Quotient 

We  must  now  pass  on  to  note  how  the  grade  of  in- 
telligence of  a  subject  can  be  derived  from  his  per- 
formances in  the  tests. 

Considering  the  problem  schematically,  we  might 
think  that  the  grade  of  intelligence  could  be  ex- 

2The  simple  set  of  materials  needed  for  carrying  on  the  German 
tests,  after  Bobertag  (lists  of  questions,  tests  of  memory  span, 
pictures,  set  of  small  boxes  for  weights,  etc.),  may  be  had  of  the 
Institute  for  Applied  Psychology  at  Klein-Glienicke. 


THE  METHOD  OF  AGE  GRADATION  37 

pressed  by  the  stage  whose  tests  could  just  be  passed 
by  the  child:  a  subject  who  readily  passed  all  the 
tests  up  through  the  9-year  ones,  but  failed  with  the 
10-year  and  subsequent  ones,  would,  accordingly, 
possess  a  nine-year  grade  of  intelligence. 

But  things  are  never  quite  so  simple  in  actuality 
as  they  are  in  theory.  The  varying  tests  of  any 
given  age-level — we  may  call  them  a.  b.  c.  d.  e, — are 
not  all  equally  difficult  for  all  children,  but  there  are, 
on  the  contrary,  quite  remarkable  individual  varia- 
tions. One  child  passes  a  to  d,  but  fails  with  e;  an- 
other passes  a,  c  and  e,  but  not  b  and  d.  This  is  due 
in  part  to  momentary  fluctuations  of  attention, 
fatigue,  etc.,  that  must,  of  course,  always  be  reckoned 
with,  but  in  part  also  to  qualitative  differences  in  in- 
telligence. The  correlation  between  the  different 
phases  of  intellectual  functions  is  truly  never  so  high 
that  a  positive  accomplishing  of  test  a  must  neces- 
sarily entail  a  like  accomplishing  of  the  approxi- 
mately 'equally  diffcult'  tests  b,  c  and  d. 

And  so  it  comes  about  that  there  is  no  hard  and 
fast  boundary  between  the  age-level  that  a  child 
passes  completely  and  the  levels  that  are  unquestion- 
ably beyond  his  powers ;  rather  is  there  an  interme- 
diate territory  of  greater  or  less  extent  within  which 
successes  and  failures  are  scattered  in  irregular 
fashion:  we  shall  call  this  the  area  of  irregularity 
(Gebiet  der  Staff  elstreuung).  It  is  impossible  to  de- 
rive a  mean  or  average  value  from  the  data  afforded 
by  this  area  without  proceeding  in  a  somewhat  arbi- 
trary manner,  but  the  formula  proposed  by  Binet 
and  Simon  seems  to  have  answered  very  well  so  far. 


38     PSYCHOLOGICAL   METHODS  OF   TESTING   INTELLIGENCE 

According  to  it,  one  first  ascertains  up  to  what 
age-level  the  tests  are  passed  without  failure  (save 
that  possible  failure  with  a  single  test  is  not  counted, 
because  such  failure  may  have  been  due  to  a  momen- 
tary lapse  of  attention).  This  age-level  is  taken  as 
the  basis,  but  every  five  tests  passed  in  levels  above 
it  are  counted  as  one  more  year.  If,  then,  a  child 
should  pass  all  tests  (save  a  single  one)  to  and  in- 
cluding the  six-year  level  and  in  addition  three  tests 
each  in  the  7th,  the  8th,  and  the  9th  year  and  one  test 
also  in  the  10th  year,  these  ten  additional  tests  would 
be  counted  as  two  years,  and  the  child  would  obtain 
for  the  net  value  of  his  intelligence,  6  +  2  years,  i.  e., 
his  intelligence  would  be  rated  as  that  of  an  8-year 
old  child. 

This  net  value  in  terms  of  which  the  total  intelli- 
gence of  the  subject  is  graded  has,  therefore,  the  sig- 
nificance of  an  age-designation :  it  indicates  that  the 
intelligence  of  the  child  tested  is  equivalent  to  the 
average  intelligence  of  the  children  of  the  age  stated. 
We  thus  arrive  at  the  concept  of  mental  age  (Intel- 
ligenzalter,  niveau  intellectuel) ,  which  is  the  cardinal 
feature  of  the  method  of  graded  tests. 

Now  mental  age  must  not,  of  course,  be  thought 
of  as  an  absolutely  unequivocal  determination  of  a 
subject's  intelligence,  but  only  as  a  very  rough  quan- 
titative characterization  of  its  value,  without  any 
implication  as  to  qualitative  differences,  because  one 
and  the  same  mental  age  can  be  figured  from  the 
most  varied  sorts  of  distribution  of  passed  and  failed 
tests.  But  this  very  thing  appears  to  constitute  an 
advantage,  rather  than  a  disadvantage  of  the  con- 
cept of  mental  age,  for  it  gives  expression  to  a  fun- 


THE  METHOD  OF  AGE  GRADATION  39 

damental  psychological  fact  (already  mentioned 
above)  that,  on  account  of  the  purely  formal  char- 
acter of  intelligence  and  the  lack  of  complete  cor- 
relation among  its  constituent  capacities,  there  never 
is  a  real  phenomenological  equivalence  between  the 
intelligence  of  two  persons:  what  we  do  have  is 
rather  a  teleological  equivalence — when  measured  in 
terms  of  the  single  function  of  all  intelligence, 
namely,  adaptation  to  new  requirements.  And  for 
this  equivalence  of  two  intelligences  mental  age  fur- 
nishes an  approximate  measure,  despite  the  fact  that 
their  equivalence  does  not  mean  their  identity. 

The  area  of  irregularity  yet  further  affects  the  computation  of 
mental  age  and  in  a  way  to  which  sufficient  attention  has  not  al- 
ways been  given.  In  order  to  equalize  possible  omissions  in  the 
lower  test-levels,  one  must  always  have  at  one's  disposal  tests  in 
higher  levels.  Now  the  original  Binet-Simon  series  comprised 
tests  up  to  13  years  only :  it  follows  that  mental  age  12  or  13  can- 
not be  correctly  computed,  for  tests  from  yet  higher  levels  might 
perhaps  have  raised  the  total  performance  to  a  higher  value.  In 
using  the  1908  Binet  series,  accordingly,  computations  ought  to  be 
carried  up  to  mental  age  eleven  only. 

The  area  of  irregularity,  again,  affords  another 
value  in  addition  to  mental  age,  viz.:  the  range  of 
irregularity  (Streuungsbreite).  A  child  whose  suc- 
cesses and  failures  are  strewn  irregularly  over  test- 
levels  from  6  to  10  years  has  the  same  mental  age,  to 
be  sure,  but  a  very  different  range  of  irregularity, 
when  compared  with  another  whose  mixture  of  suc- 
cesses and  failures  lies  in  the  7th  to  the  9th  years 
only.  Bobertag,  who  first  gave  attention  to  the  im- 
portance of  differences  in  ranges  of  irregularity, 
has  devised  a  way  of  computing  this  factor;  I  have 
myself  suggested  another  way,  but  neither  has  been 
published  as  yet. 


40     PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

Yet,  even  with  these  methods,  qualitative  differ- 
ences in  the  area  of  irregularity  are  not  touched, 
and  for  this  reason  it  will  be  necessary  in  many  cases 
to  enter  into  a  detailed  analysis  of  the  testing  as  well 
as  to  state  the  two  resultant  values  (mental  age  and 
range  of  irregularity).  It  will  often  be  distinctly 
worth  while  to  determine  in  which  tests  there  was 
special  difficulty,  in  which  special  success.  More- 
over, the  value  of  observing  the  child  during  the  test- 
ing must  not  be  underestimated,  for  in  many  of  the 
tests  there  are  ways  of  setting  about  the  task  that 
may  be  of  great  interest  (and  for  medical  or  peda- 
gogical judgment  of  the  case,  too),  though  these 
things  would  not  be  evident  in  the  mere  plus  or  minus 
set  down  for  the  outcome  of  the  tests.  We  may  al- 
lude, in  this  connection,  among  other  things,  to  the 
kind  of  description  given  to  the  pictures,  to  the  enu- 
meration of  the  60  words,  as  well  as  to  the  behavior 
of  the  child  when  he  arranges  in  order  the  five 
weights  of  like  appearance  but  unlike  weight.  In 
this  last  it  is  not  nearly  so  important  whether  the 
child  finally  gets  the  order  right  as  it  is  to  observe 
the  child's  manner  of  going  to  work — whether  and 
how  quickly  he  grasps  the  unaccustomed  problem, 
whether  he  compares  just  two  weights  each  time,  or 
compares  each  weight  with  all  the  others  when  he 
puts  it  in  place,  or  what  not.  In  these  investigations 
we  should  be  warned,  then,  against  the  bare  pursuit 
of  numerical  values :  computation  of  such  values  and 
qualitative  analysis  must  supplement  one  another, 
though,  naturally,  now  the  former  and  now  the  latter 
will  receive  special  stress,  according  to  the  setting 
of  the  problem. 


41 

But  let  us  return  to  mental  age.  The  full  signifi- 
cance of  this  final  value  is  disclosed  only  when  we 
consider  it  in  relation  to  other  circumstances.  It  can 
evidently  be  related  to  other  quantitative  scales,  like 
chronological  age,  school  grade  and  school  standing, 
or  we  can  find  out  how  it  varies  with  certain  qualita- 
tive conditions,  like  social  level,  type  of  school,  na- 
tionality and  the  like. 

Doubtless  most  significant  is  the  relation  of  mental 
age  to  the  actual  chronological  age  of  the  subject,  for, 
as  already  said,  a  certain  mental  level  goes  normally 
with  a  certain  age,  so  that  the  relation  of  mental  to 
chronological  age  indicates  the  amount  of  discrep- 
ancy between  the  intelligence  present  and  that  re- 
quired (in  the  sense  of  a  norm  to  be  expected),  and 
in  this  way  affords  an  expression  for  the  degree  of 
the  child's  intellectual  endowment. 

Up  to  now  this  discrepancy  has  always  been  com- 
puted in  the  simple  form  of  the  difference  between 
the  two  ages,  which,  when  negative  gave  the  absolute 
mental  retardation,  when  positive  the  absolute  mental 
advance  of  the  child  in  terms  of  years.  Thus,  if 
mental  retardation  —  —  2,  the  child's  mental  de- 
velopment is  two  years  behind  the  normal  level  of 
his  age. 

It  is  perfectly  clear  how  valuable  the  measurement 
of  mental  retardation  is,  particularly  in  the  investi- 
gation of  abnormal  children.  It  has,  however,  been 
shown  recently  that  the  simple  computation  of  the 
absolute  difference  between  the  two  ages  is  not  en- 
tirely adequate  for  this  purpose,  because  this  differ- 
ence does  not  mean  the  same  thing  at  different  ages 
(compare  what  is  said  in  Section  4a,  pp.  70  ff.)  .  Only 


42     PSYCHOLOGICAL   METHODS  OF   TESTING   INTELLIGENCE 

when  children  of  approximately  equal  age-levels  are 
under  investigation  can  this  value  suffice:  for  all 
other  cases  the  introduction  of  the  mental  quotient 
will  be  recommended  farther  on  (cf.  pp.  80  if.).  This 
value  expresses  not  the  difference,  but  the  ratio  of 
mental  to  chronological  age  and  is  thus  partially  in- 
dependent of  the  absolute  magnitude  of  chronological 
age.  The  formula  is,  then :  mental  quotient  =  mental 
age  -r-  chronological  age.  With  children  who  are  just 
at  their  normal  level,  the  value  is  1,  with  those  who 
are  advanced,  the  value  is  greater  than  unity,  with 
those  mentally  retarded,  a  proper  fraction.  The 
more  pronounced  the  feeble-mindedness,  the  smaller 
the  value  of  the  fraction. 

Another  and  last  concept  that  'mental  age'  sup- 
plies is  that  of  mental  arrest.  This  applies  only  to 
feeble-minded  individuals  and  means  a  mental  age 
that  is  not  exceeded,  despite  increase  of  chronolog- 
ical age. 

3.    Results  with  Normal  Children 

The  investigation  of  normal  children  forms  a  pre- 
condition of  the  whole  method,  since  the  norm  for 
each  age  must  first  be  determined  upon  them.  Yet, 
at  the  same  time,  investigations  of  these  children 
have  already  brought  out  a  series  of  results  that 
permit  us  to  set  no  slight  value  on  the  future  worth 
of  intelligence  tests  for  the  problems  of  normal  peda- 
gogy. Thus  far,  tests  have  been  made  chiefly  upon 
children  in  the  common  schools  of  both  sexes  and 
of  different  ages,  less  often  upon  pupils  of  the  higher 
schools. 


THE  METHOD  OF  AGE  GRADATION 


43 


' 


(a)  General  distribution  of  the  level  of  intelli- 
gence. In  those  investigations  where  there  have 
been  tested  a  large  number  of  elementary  school 
pupils  of  different  ages  and  with  no  attempt  at  spe- 
cial selection,  there  could  be  worked  out  general  sta- 
tistics of  the  number  of  children  that  are  at,  above 
or  below  the  mental  level  of  their  age.  I  bring  to- 
gether in  the  following  table  the  percentages  thus 
far  obtained. 

TABLE   I. 

DISTBIBUTION  OF  THE  LEVEL  OF  INTELLIGENCE  FOB  ALL  AGES 
COLLECTIVELY. 


Difference,  in  Years,  Between 

Mental    and    Chronological 

Age.  

—2 

—1 

o 

_i_i 

-1-2 

Binet  (203  Children)  

« 

91  ^ 

K1 

on  K 

1 

Bobertag  (261  Children)8  

3. 

19 

52 

22.5 

2.5 

Goddard  (1277  Children)4... 

II5 

20.5 

41.5 

21.5 

5.55 

'Children  from  5  to  10  years  old. 
*Children  from  5  to  11  years  old. 
•Includes  two  or  more  years  below  or  above  age. 

Binet  (37,  p.  112)  has  brought  together  a  frequency  distribution 
of  203  normal  children  (ages  not  given).  In  this  distribution  we 
may  note  a  remarkable  symmetry :  almost  exactly  one-half  of  the 
children  are  'at  age,'  a  good  quarter  are  'below  age,'  and  a  scant 
quarter  are  'above  age.' 

Bobertag  has  called  attention  to  this  peculiarly  simple  sym- 
metrical numerical  distribution  that  he  had  noted  first  in  his  own 
results  and  then  found  confirmed  in  Binet. 

Bobertag  has  just  published  his  own  frequency  distribution.  I 
take  from  it  (40,  II,  Table  I)  the  figures  for  261  children  between 
5  and  10  years.  While  here,  again,  the  'at  age'  children  comprise 
half  of  all  the  cases,  the  divergence  between  the  two  other  groups 
is  but  slight — the  'advanced'  are  somewhat  more  numerous  than 
the  'retarded'  children. 

A  third  set  of  data,  derived  from  a  much  more  extensive  ma- 
terial, has  been  given  us  by  Goddard  (48),  who  has  tested  all  the 
school  children  of  a  small  American  city  (Vineland,  N.  J.).  The 
distribution  curve  that  Goddard  has  prepared  from  his  raw  figures 


44    PSYCHOLOGICAL   METHODS  OF  TESTING   INTELLIGENCE 

is  certainly  not  usable,  because  lie  has  included  in  it  also  the  age- 
levels  of  12  years  and  over,  i.  e.,  children  for  whom  no  more  ade- 
quate tests  were  available  from  higher  levels ;  the  data  for  these 
subjects  must  therefore  necessarily  be  thrown  out  If  we  bring 
together  only  those  children  whose  area  of  irregularity  is  of  satis- 
factory scope,  children,  then,  between  4  and  11  years  old,  we  shall 
have  1277  children,  and  it  is  their  percentual  distribution  that  I 
have  computed.  In  it  the  percentage  of  children  'at  age'  is  some- 
what less,  that  of  children  'above  age'  is  approximately  the  same 
as  Bobertag,  while  that  of  children  'below  age'  shows  a  plain, 
though  not  very  large  increase. 

When  we  stop  to  think  that  we  have  to  do  in  these 
three  investigations  not  only  with  children  of  differ- 
ent nationality,  but  also  with  different  examiners, 
each  of  whom  had  his  own  way  of  setting  the  tests 
and  of  evaluating  them,  we  can  not  lay  great  stress 
upon  what  discrepancy  exists  between  the  three  sets 
of  statistics :  we  may  conclude  from  them  that  when 
a  sufficiently  large  number  of  non-selected  children 
of  different  ages  are  tested,  their  degree  of  intelli- 
gence will  be  distributed  in  a  somewhat  symmetrical 
fashion.  Approximately  one-half  (in  America  a 
scant  half)  stand  at  the  level  of  their  age;  about  a 
fifth  (to  a  fourth)  are  a  year  retarded  and  the  like 
number  a  year  advanced;  only  a  small  percentage 
(at  the  most  11  per  cent.)  show  more  than  one  year 
of  retardation  and  a  still  smaller  fraction  (at  the 
most  5.5  per  cent.)  is  mentally  advanced  by  more 
than  one  year. 

One  must  be  careful  not  to  regard  the  'at  age' 
child  and  the  'normal'  child  as  synonymous  terms: 
on  the  contrary,  the  statistical  results  themselves 
show  that  the  '  at  age '  children  simply  constitute  the 
middle  section  of  normality,  while  the  children  that 
are  one  year  advanced  or  retarded  are  still  com- 
pletely within  the  bounds  of  normality. 


THE  METHOD  OF  AGE  GRADATION  45 

It  is  worth  noting  that  the  distribution  just  cited  bears  a  cer- 
tain resemblance  to  the  simplest  type  of  distribution  known  as 
Gauss'  frequency  curve,  for  this  latter  is  not  only  a  symmetrical 
curve,  but  it  is  also  divided  by  the  value  known  as  the  'probable 
error'  into  three  sections,  and  in  such  a  manner  that  the  middle 
section  comprises  the  half,  and  the  two  end-sections  each  one- 
quarter  of  all  the  cases.  Even  a  generation  ago  Galton  advanced 
the  hypothesis  that  the  abilities  of  a  large  group  of  non-selected 
individuals  would  be  distributed  symmetrically  in  the  form  of  the 
Gaussian  curve.  It  is  true  that  Galton  thought  the  Gaussian  law 
of  distribution  could  be  extended  to  apply  to  a  very  detailed 
gradation  (16  grades)  of  ability,  whereas  statistics  at  present 
available  only  make  it  probable  for  a  few  main  groups. 

Bobertag  has  supplemented  our  knowledge  of  this 
matter  by  discovering  that  a  similar  distribution 
holds  good  on  other  occasions  when  a  fairly  large 
number  of  individuals  is  divided  into  good,  medium 
and  poor  groups.  In  statistics  of  marks  pertaining 
to  2772  pupils,  it  turned  out  that  marks  of  "better 
than  satisfactory"  were  assigned  to  25.7  per  cent., 
of  "  satisfactory "  to  50.8  per  cent.,  and  of  "  unsatis- 
factory" to  23.5  per  cent,  of  all  cases  (40,  IT, 
Table  IV). 

Yet  it  is  well  not  to  ascribe  too  great  significance 
to  these  ratios  of  distribution.  In  the  first  place, 
the  empirical  data  now  at  our  disposal  are  not 
enough  to  warrant  as  yet  the  assumption  of  a  gen- 
eral conformity  to  law;  and  even  for  the  data  now 
at  our  disposal  the  formula  holds  only  as  a  rough 
approximation  and  merely  as  a  general  tendency  for 
a  rather  large  number  of  cases  within  which  the 
numerous  irregularities  compensate  each  other 
(compare  on  this  point  the  next  section).  Neverthe- 
less, the  findings  already  secured  are  of  sufficient  in- 
terest to  be  followed  up  farther.6 

"Further  discussion  of  this  principle  of  symmetrical  distribution 
and  its  relation  to  the  Gaussian  curve  may  be  found  in  one  of  my 
previous  articles  (I,  248  ff.)  and  in  Bobertag  (40,  II). 


46     PSYCHOLOGICAL   METHODS   OF   TESTING    INTELLIGENCE 

The  principle  governing  this  distribution  has,  how- 
ever, heuristic  value  even  now  in  two  ways:  (1) 
When  we  are  obliged  to  divide  a  group  of  persons  on 
the  basis  of  their  mental  ability  into  a  good,  a  me- 
dium, and  a  poor  group,  the  convenient  and  common 
division  into  three  groups  of  equal  size  is  certainly 
less  close  to  the  actual  gradations  than  the  setting 
off  of  a  good  and  a  poor  quarter  from  the  homoge- 
neous middle  half  of  medium  ability.  (2)  A  require- 
ment, e.  g.,  of  a  test  or  of  a  series  of  tests,  may  stand 
as  normal  for  a  given  group  of  individuals  when  ap- 
proximately 75  per  cent,  of  the  members  of  the  group 
meet  it  in  a  satisfactory  or  more  than  satisfactory 
manner.  This  idea  has  been  used  by  Bobertag7  for 
the  standardization  of  tests. 

(b)  Different  age-levels  and  nationalities.  God- 
dard  has  thought  that  the  symmetry  of  the  curve  of 
which  we  have  just  been  speaking  might  be  deemed 
proof  that  the  Binet-Simon  arrangement  of  tests 
represents  in  a  way  an  ideal  series,  because  it  has  af- 
forded on  empirical  test  a  distribution  that  was 
theoretically  to  have  been  expected.  But  this  con- 
clusion is  unjustifiable.  The  curve  of  symmetry  ap- 
plies primarily  only  to  all  children  taken  collec- 
tively, without  regard  to  age;  but  the  Binet-Simon 
tests  should  really  embrace  normal  standards  for 
children  of  every  one  of  the  series  of  ages  and  their 
correctness  would  be  demonstrated  only  provided 
the  symmetrical  distribution  were  disclosed  for 
normal  unselected  children  of  each  single  year.  But 
this  is  by  no  means  the  case,  and,  as  a  matter  of  fact, 


TSee  Section  5a  for  details. 


47 

least  of  all  in  Goddard's  own  results.  Bather  is  it 
true,  as  is  evident  from  closer  consideration,  that 
the  symmetrical  curve  above  mentioned  owes  its 
existence  to  the  fact  that  the  varying  results  of  dif- 
ferent years  practically  compensate  each  other.8  In 
truth,  the  results  of  almost  all  who  have  tried  out 
the  Binet-Simon  method,  regardless  of  the  nation- 
ality tested,  agree  that  the  series  set  for  the  lower 
years  are  too  easy,  those  for  the  higher  too  difficult. 
The  evidence  for  this,  so  far  as  known  to  me,  I  have 
introduced  in  Table  II. 

From  Goddard's  (48,  p.  243),  Bobertag's  (40,  II,  Table  I)  and 
Miss  Johnstone's9  raw  tables  I  have  computed  the  percentages  of 
frequency  for  American,  German  and  English  children.  Goddard's 
data  I  have  figured  for  each  year  separately ;  those  for  the  two 
other  investigators  by  bringing  two  or  three  years  together,  on 
account  of  the  smaller  number  of  cases  (Table  II).  It  will  be 
seen  that  in  the  lower  years  many  more  are  'advanced'  than  there 
should  be:  in  Goddard  and  in  Johnstone  the  advanced  outnumber 
not  only  the  retarded,  but  even  the  'at-age'  children.  Thus,  for 
instance,  in  Goddard  more  than  half  the  5-year  old  children  attain 
a  mental  age  of  6  years  or  over — clear  evidence  that  these  tests 
are  much  too  easy.  In  Bobertag  the  lack  of  symmetry  is  not  so 
pronounced. 

The  area  of  excessive  percentage  of  advanced  children  (and  thus 
of  excessive  ease  of  the  tests )  extends  in  Goddard  through  the  7th, 
in  Bobertag  through  the  8th  year ;  in  Johnstone  it  has  not  en- 
tirely disappeared  even  at  the  9th  year.  Then  comes  a  sudden  re- 
versal :  in  the  higher  years  the  number  of  retarded  children  in- 
creases :  the  tests  are  therefore  too  hard. 

With  the  155  subjects  examined  by  Bloch  and  Preiss  (38)  there 
was  made  at  the  outset  a  selection  such  that  only  children  of 
medium  ability  and  school  performance  were  tested.  Consequently, 
retardation  in  mental  age  appeared  almost  not  at  all,  but  advance 
did  appear,  though  in  diminishing  frequency  with  advancing  age. 

"Ayres  (31)  calls  attention  to  this  point  in  his  critique  of 
Goddard. 

•In  Miss  Johnstone's  original  work  (52)  the  quantitative  data 
are  not  given  sufficiently  clearly,  but  these  data  are  given  by 
Binet  (3G,  p.  196)  where  will  be  found  a  table  of  distribution  for 
146  Sheffield  school  girls  as  imparted  in  a  letter  from  Miss  John- 
stone. 


48    PSYCHOLOGICAL   METHODS  OP  TESTING  INTELLIGENCE 

From  the  data  given  it  can  be  computed  that  there  were  above  the 
level  of  their  age  a  full  50  per  cent  of  the  7-year  olds,  20  per  cent, 
of  the  8  and  9-year  olds  and  only  14  per  cent,  of  the  10  and  11-year 
olds. 

TABLE  n. 

PEBCENTAGES  BETARDED,   AT  AGE  AND  ADVANCED  AT  DIFFERENT  YEABS. 

Chronological 

Investigator          Age  Retarded  At  Age  Advanced 

5  12  35  53 

6  20.5  30  49.5 

7  13  58  29 
Goddard.  ....-{         8                   44                      41  15 

9  40  28  32 

10  27.5  56  16.5 

11  56  36  8 

5-6  11  60  29 

Bobertag -j      7-8  7  48.5  44.5 

9-11  34  50  16 

6-7  12  20  68 

Johnstone.  .  .  .  -(      8-9  20  40  40 

10-11  62  25  13 

In  the  work  of  the  Americans,  Terinan  and  Childs  (64),  and  of 
Mile.  Descoeudres  (46),  of  Geneva,  we  find  another  method  of 
presenting  data,  but  the  same  result.  The  first-named  tested  396 
unselected  children  and  figured  the  average  value  of  each  age; 
they  found  that  the  young  children  attained  a  much  too  high  level, 
the  older  children  a  too  low  average  level  of  intelligence,  so  that, 
on  the  whole,  the  mental  levels  were  more  like  one  another  than 
were  the  chronological  levels.  It  follows  that  the  tests  fail  to 
bring  fully  to  light  the  actual  differences  between  the  children. 
Mile.  Descoeudres  had  tested  in  all  only  24  children  of  six  different 
ages;  the  results  showed  differences  of  only  two  to  four  years  in 
the  mental  ages  of  children  in  the  youngest  and  oldest  groups, 
though  the  chronological  ages  differed  by  six  years. 

All  these  findings  show,  first  of  all,  that  the  ar- 
rangement of  the  tests  set  forth  by  Binet  and  Simon 
in  1908  suffer  from  not  inconsiderable  errors  that 
must  be  removed.  Binet  himself  has  recognized 
these  defects,  too,  at  least  in  part,  for  he  subse- 
quently relegated  the  tests  for  11,  12  and  13-year 
subjects  to  higher  age-levels. 


THE  METHOD  OP  AGE  GRADATION  49 

TABLE  HI. 
AVEEAGES  FOB  CEBTAIN  YEABS.   (TEBMAN  AND  CHILDS.) 

Chronological  Age  Mental  Age 
4.75  6.50 

7.50  8.00 

12.33  11.00 

But  far  more  important  is  a  positive  result,  viz. : 
the  international  accordance  in  the  judgment  as  to 
special  ease  or  special  difficulty  of  certain  test-levels. 
It  is  certainly  not  of  minor  significance  that  the  6- 
year  old  tests  were  too  easy  and  the  11-year  old  as 
uniformly  too  difficult,  with  the  8  and  9-year  old  ap- 
parently forming  a  between-lying  zone  in  the  case 
of  children  in  the  common  schools  of  America,  Ger- 
many, France  and  England,  all  without  exception. 
That,  despite  the  differences  in  race  and  language, 
despite  the  divergences  in  school  organization  and 
in  methods  of  instruction,  there  should  be  so  decided 
agreement  in  the  reactions  of  the  children — is,  in 
my  opinion,  the  best  vindication  of  the  principle 
of  the  tests  that  one  could  imagine,  because  this 
agreement  demonstrates  that  the  tests  do  actually 
reach  and  discover  the  general  developmental  condi- 
tions of  intelligence  (so  far  as  these  are  operative  in 
public  school  children  of  the  present  cultural  epoch), 
and  not  mere  fragments  of  knowledge  and  attain- 
ments acquired  by  chance. 

And  this  confirmation  of  the  principle  may  also 
lead  us  confidently  to  expect  that  the  discrepancies 
that  have  been  revealed  at  the  same  time  in  some  of 
the  details  of  the  system  can  be  obviated  in  the 
future. 


50     PSYCHOLOGICAL   METHODS   OP   TESTING   INTELLIGENCE 

(c)  Children  of  different  social  strata.  Social 
differences  turn  out  otherwise  than  do  differences 
of  nationality,  for  they  come  out  more  or  less  con- 
spicuously in  the  results  of  the  tests.  The  task  of 
making  comparative  investigations  by  the  graded 
tests  of  children  of  different  social  levels  was  under- 
taken in  1910  by  Binet  (36,  p.  187)  and  by  Breslau 
teachers,  simultaneously. 

The  incentive  that  led  Binet  to  undertake  this 
problem  arose  in  certain  investigations  conducted 
by  Decroly  and  Mile.  Degand  in  a  private  school  at 
Brussels  (45),  the  results  of  which  seemed  to  cast  a 
measure  of  doubt  upon  the  value  of  Binet 's  tests, 
since  the  tests  turned  out,  all  of  them,  to  be  too  easy. 
To  be  explicit,  of  45  children  tested,  no  one  was  be- 
low, 9  were  at,  and  the  rest  were  above  the  level  of 
their  age  (13  by  one  year,  17  by  two  years,  and  9 
even  by  three  years).10  Binet  now  points  out,  and 
rightly,  that  these  figures  present  no  argument  what- 
soever against  the  value  of  his  tests,  but  merely  af- 
ford a  positive  contribution  to  the  study  of  the  dif- 
ferentiation conditioned  by  social  factors.  For  all 
these  Belgian  children  were  sprung  from  the  circles 
of  the  cultured  middle  class,  whereas  the  Parisian 
children  to  whom  the  tests  were  'fitted'  belonged 
to  lower  classes.  Binet,  on  this  basis,  reckons  the 
average  difference  in  mental  age  between  children 
of  the  higher  and  lower  classes  at  approximately  a 
year  and  a  half.  Of  course,  this  figure  can  stand 
only  as  a  rough  approximation ;  it  will  vary,  partic- 
ularly at  different  levels  of  chronological  age — a 

10See  the  review  by  Bobertag,  Zeits.  f.  angew.  Psych.,  5 :  p.  205, 


THE  METHOD  OF  AGE  GRADATION  51 

point  to  which  Biiiet,  unfortunately,  does  not  refer. 
Binet,  himself,  also  induced  some  school  directors 
of  his  acquaintance  to  take  up  this  question  in 
Paris.  As  a  matter  of  fact,  children  in  the  superior 
schools  were  not  considered,  and  the  attempt  was 
made  merely  to  ascertain  whether  an  influence  of 
social  environment  could  be  discerned  ivithin  the 
common  schools.  It  is  to  be  regretted  that  these 
tests  were  carried  out  upon  but  an  extraordinarily 
small  number  of  children. 

One  investigation  (p.  194)  that  was  restricted  to  a  single  school 
came  to  no  result.  In  this  study  there  were  examined  54  children, 
classified  into  four  groups  on  the  basis  of  social  status.  It  may  be 
mere  accident  that  relatively  more  advanced  children  were  found 
among  the  poorest  than  among  the  other  groups;  but  at  any  rate 
there  was  no  trace  of  any  positive  relationship  between  mental 
age  and  social  position.  Probably,  as  Binet  himself  has  already 
pointed  out,  the  social  differences  present  in  this  study  were  too 
small  to  affect  the  outcome. 

TABLE   IV. 
DISTRIBUTION  OF  TWO  GROUPS   OF  30  PUBLIC   SCHOOL  CHILDREN   EACH. 

, — Retarded — ^  > — Advanced — \ 

2  Years    1  Year  At  Age  1  Year     2  Years 

Poor  Neighborhood 1             11  13  4             1 

Good  Neighborhood. ...     1                3  10  10              G 

On  the  other  hand,  a  clear  difference  was  revealed 
when  comparison  was  made  of  two  public  schools 
(p.  198),  one  of  which  was  situated  in  the  poorest 
quarter,  the  other  in  a  relatively  well-to-do  neigh- 
borhood of  Paris.  There  were  tested  from  each 
school  30  children  of  corresponding  ages,  selected 
without  reference  to  their  school  performance. 
Table  IV  shows  how  much  more  numerous  were  the 
cases  of  retarded  intelligence  in  the  poorer  school. 
Binet  figures  the  average  superiority  in  mental  age 


52    PSYCHOLOGICAL   METHODS  OF  TESTING   INTELLIGENCE 

of  the  children  of  the  better  situated  school  to  be 
three  quarters  of  a  year.11 

A  question  as  interesting  as  it  is  difficult  to  answer 
arises  when  we  seek  the  causes  of  these  differences 
in  performance.  It  would  obviously  be  very  prema- 
ture to  assume  as  already  positively  demonstrated 
that  the  intelligence,  considered  as  innate  mental 
ability,  was  of  lower  grade  in  children  of  the  lower 
and  poorer  classes.  Of  course,  it  is  not  impossible 
that  this  may  have  been  operative  as  a  causal  factor. 
One  might,  perhaps,  assume  that  the  very  rise  into 
the  higher  and  better-off  classes  would  itself  predi- 
cate a  certain  intellectual  selection,  and  that  thus 
the  children  of  these  classes  would  have  come  into  the 
world  equipped  with  a  superior  intellectual  endow- 
ment. 

But,  on  the  other  hand,  it  must  be  remembered 
that  no  series  of  tests,  however  skillfully  selected  it 
may  be,  does  reach  the  innate  intellectual  endow- 
ment, stripped  of  all  complications,  but  rather  this 
endowment  in  conjunction  with  all  the  influences  to 

"Since  Stern  assembled  this  material  there  has  appeared  an 
American  study  that  does  not  confirm  the  general  principle  of  en- 
vironmental influence  (J.  Weintrob  and  R.  Weintrob.  The  Influ- 
ence of  Environment  on  Mental  Ability  as  Shown  by  Binet-Simon 
Tests.  Jour,  of  Educ.  Psych.,  3:  1912,  577-583).  The  subjects 
were  210  children,  70  from  the  Horace  Mann  School  of  Teachers 
College,  Columbia  University,  representing  children  from  wealthy, 
or  at  least  very  well-to-do  families,  70  from  the  Speyer  School, 
representing  families  of  the  "comfortable  middle  class"  (wage- 
earners  and  small-business  men),  and  70  from  the  Hebrew  Shelter- 
ing Orphan  Asylum  of  New  York,  who  were  children  springing 
from  a  very  unfavorable  environment.  While  the  relatively  small 
number  of  cases  and  the  difference  of  nationality  may  render  the 
outcome  less  conclusive,  the  results  from  the  thre^e  institutions 
"showed  very  small  and  inconsistent  differences."  The  original 
article  should  be  consulted  for  further  analysis  of  the  data. — 
Translator. 


53 

which  the  examinee  has  been  subjected  up  to  the 
moment  of  the  testing.  And  it  is  just  these  external 
influences  that  are  different  in  the  lower  social 
classes.  Children  of  higher  social  status  are  much 
more  often  in  the  company  of  adults,  are  stimulated 
in  manifold  ways,  are  busy  in  play  and  amusements 
with  things  that  require  thinking,  acquire  a  totally 
different  vocabulary  and  a  notable  command  of  lan- 
guage, and  receive  better  school  instruction ;  all  this 
must  bring  it  about  that  they  meet  the  demands  of 
the  tests  better  than  children  of  the  uncultured 
classes. 

Presumably,  each  of  these  factors,  internal  and 
external,  endowment  and  environmental  influences, 
plays  a  role  in  the  result ;  but  we  shall  have  to  wait 
until  very  many,  more  extensive  investigations  have 
been  made  before  we  can  secure  more  exact  knowl- 
edge of  the  actual  amount  and  range  of  influence 
possessed  by  the  one  or  the  other  of  them.  The  way 
to  approach  this  problem  is  by  special  analysis  of 
the  data:  it  will  be  necessary  to  find  out  in  which 
tests  the  superiority  of  the  children  of  the  cultured 
classes  is  particularly  evident  and  which  tests  are 
passed  with  equal  facility  by  children  of  both  classes. 

The  material  for  a  preliminary  comparison  of  this  sort  has  been 
drawn  by  Binet  (36,  p.  191)  from  the  tables  of  Decroly  and 
Degand.  In  them  it  is  very  interesting  to  note  that  the  special 
superiority  shown  by  better  situated  children  is  in  those  tests  that 
involve  thinking  in  the  true  sense  of  the  term — apprehension,  com- 
parison, criticism,  formation  of  concepts,  synthesis,  etc.,  though, 
it  must  be  admitted,  most  of  them  put  a  premium  on  linguistic 
readiness.  Tlj*  tests  here  included  are:  description  and  explana- 
tion of  pictures,  comparison  of  two  objects,  definition  of  abstract 
terms,  recognition  of  omissions  in  drawings,  criticism  of  absurd 
statements,  arrangements  of  the  five  weights,  naming  60  words  in 
three  minutes.  To  these  are  to  be  added  certain  tests  that  ob- 


54     PSYCHOLOGICAL    METHODS   OF   TESTING   INTELLIGENCE 

viously  depend  more  upon  external  circumstances,  like  knowing 
the  days  of  the  week,  the  months  of  the  year  and  coins.  On  the 
other  hand,  the  tests  that  Binet  designates  as  revealing  social  dif- 
ferences only  slightly  are  for  the  most  part  those  that  hinge  on 
school  instruction,  as  copying,  writing  from  dictation,  counting 
backwards,  making  change,  drawing  a  diamond.  Only  a  single  one 
of  the  tests  that  fail  to  reveal  social  differences  is  a  real  test  of 
intelligence — the  completion  of  gaps  in  a  text.  However,  in  view 
of  the  small  number  of  children  that  could  be  used  to  base  these 
results  upon,  any  generalization  of  the  conclusions  from  them  is 
to  be  avoided. 

This  problem  of  social  differences  and  their  effect 
upon  intelligence  leads  over  directly  to  certain  prac- 
tical pedagogical  principles.  We  may  think,  in  this 
connection,  for  instance,  of  the  demand  [in  Ger- 
many] for  the  establishment  of  the  'common'  school 
(Einheitsschtde),  in  which  children  of  all  classes  of 
society  shall  be  included  without  distinction.12  It 
seems  to  me  that  in  the  discussion  of  this  problem, 
just  as  in  the  problem  of  co-education,  the  purely 
psychological  presuppositions  are  kept  too  little 
in  mind  because  the  socio-ethical  phase  of  the  ques- 
tion tends  to  claim  first  attention. 

But  how  the  psychological  methods  of  testing  in- 
telligence can  become  of  direct  service  for  these 
practical  questions  will  be  shown,  I  hope,  by  an  in- 
vestigation with  the  Binet-Sinion  tests  that  is  now 
being  undertaken  by  a  group  of  teachers  in  Breslau. 
The  problem  under  study  is  that  of  a  systematic 
comparison  of  pupils  in  a  Volksschule  and  those  in  a 
Vorschule,  i.  e.,  the  younger  pupils  in  the  Vorschule 
of  a  Gymnasium.13  The  aim  is  to  find  out  whether 

12See  the  footnote  on  p.  55. — Translator. 

"As  it  is  impossible  to  render  these  terms  in  English  equiva- 
lents, it  is  proper  to  explain  that  the  German  Volksschule  is  the 
elementary  public  school  attended  by  children  of  the  laboring  or 
lower  business  classes.  In  it  attendance  is  absolutely  compulsory 


THE  METHOD  OF  AGE  GRADATION  55 

there  exist  typical  differences  of  intelligence  be- 
tween groups  of  children  of  the  same  age,  and  what 
magnitude  these  differences  attain  at  different  ages. 
In  Prussia  pupils  may  enter  the  Sexta  (lowest  class) 
of  the  Gymnasium  after  three  years  in  the  Vorschule, 
but  only  after  four  years  in  the  Volksschule.  The 
tests  were  also  aimed  to  discover  to  what  extent  this 
rule  is  psychologically  justified,  not  only  by  the  dif- 
ferences in  the  curricula  of  the  two  schools,  but  also 
by  the  general  mental  maturity  of  the  children. 

Five  groups  were  tested  that  had  been  carefully 
planned  to  be  comparable  in  the  matter  of  age,  viz. : 
7  and  9  year  old  pupils  of  the  Vorschule,  and  7,  9  and 
10  year  old  pupils  in  the  Volksschule — in  all  about 
150  boys.  (See  above,  pp.  35  f.,  for  some  of  the  pre- 
cautionary rules  observed  in  testing) .  The  results  are 
now  being  worked  out ;  but,  thanks  to  the  courtesy 
of  the  investigators,  I  have  been  able  to  get  some  of 


from  6  to  14,  unless  the  child  is  otherwise  instructed.  The  Gym- 
nasium is  one  of  a  number  of  so-called  'higher'  or  'secondary* 
schools  with  a  9-year  curriculum  (ages  9  to  18,  or  more),  and 
preparatory  for  entrance  into  the  university.  Children  of  the  bet- 
ter classes,  destined  for  higher  education,  enter  the  Gymnasium 
(or  some  variant  of  it)  after  a  preliminary  three-year  training 
(ages  6  to  9)  in  a  Vorschule,  which  is  thus  virtually  a  special  ele- 
mentary school  for  better-class  children.  Relatively  infrequently 
do  children  started  in  the  Volksschule  later  enter  the  Gymnasium. 

A  demand  is  now  being  made  by  certain  interests  in  Germany 
for  the  abolishment  of  these  distinctions,  at  least  in  part,  by  com- 
pelling all  children  to  begin  school  instruction  in  the  same  school 
(Einheitsschule) — a  proposal  which  has  been,  and  is,  the  occasion 
of  very  active,  and  even  bitter  discussion. 

I  have  given  a  somewhat  fuller  explanation  of  the  German 
school  system  in  Appendix  II  of  my  translation  of  Offner's  Mental 
Fatigue,  an  earlier  number  of  this  series  of  Educational  Psy- 
chology Monographs. — Translator. 


56 

them  now,  and  from  them  I  have  prepared  the  fig- 
ures that  appear  in  Table  V.  These  figures,  which 
must  be  regarded  as  strictly  provisional,  merely  in- 
dicate with  what  percentual  frequency  all  the  tests, 
taken  collectively,  for  which  I  have  the  data,  have 
been  passed,  and  this,  it  should  be  noted,  for  the 
three  older  groups  of  children  only.14 

TABLE  V. 
PERCENTAGE  OF  TESTS  PASSED  IN  CEETAIN  AGE-LEVELS  AT  BBESLA0. 

9-12  9  and  10  11  and  12 

9- Year  Vorschule  Pupils 70  77  64 

9-Year  Volksschule  Pupils 60  81  34 

30- Year  Volksschule  Pupils 70  86  46 

The  first  column  shows  that  the  9-year  old  Volks- 
schule pupils  rank  in  the  number  of  tests  passed  10 
per  cent,  below  the  pupils  of  the  same  age  in  the  bet- 
ter school,  while  the  10-year  old  Volksschule  pupils 
attain  the  same  measure  of  success  as  the  Vorschule 
pupils  a  year  younger.  That,  however,  there  is  no 
real  equality  in  this  relationship  is  shown  by  the  two 
other  columns  in  which  the  percentage  for  the  easier 
tests  (9  and  10  levels)  and  the  harder  ones  (levels  11 
and  12)  are  calculated  separately.  While,  in  the 
easier  tasks  the  Vorschule  pupils,  curiously  enough, 
rank  a  little  below  the  Volksschule  pupils  of  their 
own  age  and  9  per  cent,  below  the  older  pupils  in 
that  school,  the  outcome  is  quite  different  when  we 
pass  to  the  harder  tasks  (third  column).  These 
tests  which  lie  above  the  age-level  of  the  subjects 
are  passed  by  the  Vorschule  pupils  nearly  twice  as 
well  as  by  their  mates  of  like  age  in  the  Volksschule, 

"For  many  very  important  tests,  as  for  instance,  description  of 
the  pictures,  no  results  are  at  my  disposal  yet. 


THE  METHOD  OF  AGE  GRADATION  57 

and  even  the  older  pupils  in  these  tests  fall  18  per 
cent,  behind  the  younger  children  of  the  better 
school.  If  this  interesting  result  should  be  con- 
firmed again  in  the  detailed  computations,  as  it  prob- 
ably will  be,  we  should  then  say :  children  of  differ- 
ent social  classes  differ  from  each  other  less  in  the 
performances  appropriate  to  their  age  than  in  the 
mastery  of  tasks  that  really  lie  above  their  level. 
We  would  have,  then,  a  numerical  demonstration  for 
that  well-known  early  ripening  of  children  of  the 
higher  classes,  for  the  anticipation  of  phenomena  of 
developmental  stages  yet  to  come  before  the  content 
of  the  current  stage  of  development  is  fully  ex- 
hausted. 

We  may  look  forward  with  interest  to  the  final  re- 
sult of  these  investigations. 

The  material  of  Table  V  also  furnishes  further 
confirmation  of  a  law  of  differential  psychology :  the 
more  complex  a  mental  function,  the  more  difficult 
to  bring  it  into  action,  the  later  its  appearance  in 
the  course  of  development,  then  so  much  the  greater 
is  its  variability,  and  so  much  the  more  definitely  are 
men  and  groups  of  men  differentiated  by  it  (cf.  1, 
pp.258  and  269). 

(d)  Intelligence  and  school  performance.  The 
relation  of  these  two  factors  is  easily  the  most  im- 
portant problem  presented  by  our  theme  for  prac- 
tical pedagogy.  For  at  this  point  we  may  hope  to 
get  an  insight  into  the  factors  that  condition  the 
progress  of  children  within  the  school,  the  place  that 
they  take  among  their  fellow-pupils  on  the  basis  of 
their  work,  and  the  way  their  marks  turn  out.  Peo- 
ple are  generally  inclined  to  think  there  is  a  very 


58     PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

close  connection  between  intellectual  ability  and 
school  ability:  good  pupils  are  forthwith  regarded 
as  intelligent,  and  good  school  work  is,  with  a  cer- 
tain obviousness,  expected  of  intelligent  children, 
poor  school  work  of  the  poor  groups.  So  long,  of 
course,  as  we  had  no  special  means  of  testing  intelli- 
gence, there  was  no  foundation  on  which  to  build  up 
more  exact  knowledge  of  these  interrelations:  we 
had  to  content  ourselves  with  opinions  and  with  the 
generalization  of  occasional  observations. 

But  now  we  are  beginning  to  get  on  firmer  ground. 
Tests  of  intelligence  have  already  taught  us  that  the 
relations  between  intelligence  and  school  ability  arei 
by  no  means  so  strict  and  uniform  as  most  persons! 
had  thought.    Just  here  we  are  concerned  with  the 
conclusions  reached  by  the  Binet-Simon  method  with 
normal  children,  but  we  shall  encounter  the  same  re- 
sult later  on  in  two  places  (II,  4c  and  III,  3). 

We  have  two  measures  for  the  school  capacity  of  a 
child  that  we  want  to  compare  with  his  intelligence — 
his  pedagogical  age  and  his  marks. 

Pedagogical  age  is  the  normal  age  of  the  class  to 
which  the  child  belongs.  If  we  assume  that  school- 
ing begins  at  6,  then  the  pedagogical  age  of  a  class 
that  is  just  entering  upon  its  fourth  school  year  is 
6  +  3  =  9  years.  If  there  is  in  tin's  class  a  child  11 
years  old,  he  then  has  a  pedagogical  retardation  of 
two  years,  while  an  8-year  old  classmate  has  an  ad- 
vancement, or  acceleration,  of  one  year.  The  latter 
is  very  rare  with  us,  on  account  of  the  exact  way  in 
which  promotions  are  regulated;  cases  of  it  appear 
mostly  when  a  child  enters  after  private  prepara- 
tion or  from  another  school.  Outside  of  Germany 


THE  METHOD  OF  AGE  GRADATION  59 

cases  of  pedagogical  advance  seem  to  be  more  com- 
mon. Eetardations  are,  however,  quite  frequent  in 
consequence  of  non-promotion,  long  illness,  etc.,  and 
sometimes  they  reach  a  considerable  degree. 

Comparisons  of  pedagogical  and  mental  age  have 
been  made  by  Binet  and  by  Goddard. 

TABLE  VI. 
RELATION  OF  PEDAGOGICAL  AND   MENTAL  AGE    (BINET). 


-Mental  Age- 


Pedagogical  Age  Retarded  At  Level  Advanced  Total 

Retarded 14  9  1  24 

Normal 16  33  16  65 

Advanced 0  5  7  12 

Total 30  47  24  101 

Binet  (36,  p.  162)  presents  a  distribution-table  for 
101  pupils  and  regards  the  agreement  as  tolerably 
satisfactory  (Table  VI).  In  fact,  we  do  note  that 
there  are  no  paradoxical  cases :  no  one  of  the  children 
with  mental  retardation  is  pedagogically  advanced, 
and  only  a  single  mentally  advanced  child  turns  out 
to  be  pedagogically  retarded  (and  that  case  may  be 
conditioned  by  illness).  Yet  in  the  remainder  of  the 
Table  there  are  divergences  of  considerable  magni- 
tude: only  a  scant  third  of  the  mentally  advanced 
are  also  pedagogically  advanced;  less  than  half  of 
the  mentally  retarded  are  likewise  pedagogically  re- 
tarded, while,  of  the  pupils  'at  age'  pedagogically, 
one  quarter  surpass  and  another  quarter  fall  short 
of  the  mental  level  of  their  age. 

An  exact  computation  of  these  relations  can  be 
made  by  using  the  method  of  contingency.15  Con- 

"The  formula  for  it  is  developed  in  another  of  my  treatises 
(1,308  ff.). 


60     PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

tingency  means  the  degree  of  correspondence  be- 
tween t\vo  intersecting  groups.  If  all  children 
pedagogically  retarded  should  also  exhibit  mental 
retardation,  or  if  the  converse  should  occur,  then  the 
contingency  would  be  absolute  (—  1) ;  if  among  the 
pedagogically  retarded  children  there  were  rela- 
tively no  more  mentally  retarded  than  among  the 
children  with  normal  or  with  superior  school  attain- 
ments, then  the  contingency  would  be  =  0.  The  de- 
gree of  correspondence  can  be  shown  by  a  number 
lying  between  0  and  1,  termed  the  coefficient  of  con- 
tingency. 

From  the  above  tables  I  have  computed  the  follow- 
ing values : 

Degree  of 

First  Factor  Second  Factor  Correspondence 

Pedagogical  retardation    Mental  retardation  0.41 

Mental  retardation  Pedagogical  retardation  0.30 

Pedagogical  advance         Mental  advance  0.45 

Mental  advance  Pedagogical  advance  0.19 

The  index  of  correspondence,  then,  is  but  moder- 
ately large  at  best  and  even  that  only  when  we  pass 
from  school  ability  to  intelligence,  not  in  the  re- 
verse direction.  Hence,  to  draw  conclusions  about 
school  status  from  varying  intellectual  abilities  is 
even  less  permissible  than  to  draw  conclusions  about 
intellectual  ability  from  varying  school  status. 

In  his  mass-experiment,  Goddard  (48)  came  to  a 
similar  result.  He  found  that  more  than  the  half  of 
all  the  children  tested  were  in  classes  that  did  not 
correspond  to  their  mental  age — most  of  them,  as  a 
matter  of  fact,  in  a  lower  and  only  a  few  in  a  higher 
class. 

Bobertag  compared  mental  age  with  the  school 


THE   METHOD  OF  AGE  GRADATION  61 

marks  (40,  II,  p.  501,  Table  II).  In  his  table  of  dis- 
tribution (Table  VII),  too,  there  are  no  paradoxical 
cases.  As  for  the  rest,  the  coefficients  of  contin- 
gency are,  according  to  my  calculation,  higher  than 
with  Binet,  but  still,  however,  of  only  moderate  mag- 
nitude : 


•Mental  Age- 


School  Marks                 Retarded  At  Level  Advanced  Total 

Poor 29                  17                 0  46 

Satisfactory 26                 79               21  126 

Good 0                  13                31  44 

Total 55  109  52  216 

Second  Factor  Correspondence 
Mental  retardation  0.52 

Poor  marks  0.40 

Mental  advance  0.59 

Good  marks  0.47 

Here,  again,  it  appears  that  inference  from  school 
performance  to  mental  ability  is  safer  than  from 
mental  ability  to  school  performance,  though  here 
the  correspondence  between  intelligence  and  the 
school  performance  is  not  so  slight  as  with  Binet,  as 
above  cited. 

What,  now,  is  the  significance  of  this  lack  of  com- 
plete agreement  between  school  efficiency  and  the 
outcome  of  the  tests  of  intelligence  f 

In  the  first  place  one  might  say  that  this  was  an- 
other proof  of  the  defectiveness  of  the  tests.  That, 
since  pedagogical  age  and  school  marks  are  the  con- 
densed formulation  or  expression  of  the  long-con- 
tinued and  many-sided  efficiency  of  the  child  and 
hence  much  more  characteristic  than  the  outcome  of 


62    PSYCHOLOGICAL   METHODS  OP  TESTING   INTELLIGENCE 

a  half-hour's  testing,  we  would  place  confidence  in 
the  latter  only  if  it  agreed  with  the  former;  that  if 
it  did  not,  then  the  tests  or  at  least  the  gradation 
derived  from  them  would  amount  to  nothing. 

Now  we  have  already  alluded  in  what  has  gone 
before  to  the  weakness  of  the  gradations  of  intelli- 
gence discovered  by  the  Binet-Simon  method,  and 
it  is  entirely  probable  that  this  insufficiency  has  con- 
tributed in  part  to  the  lack  of  agreement  with  school 
performances.16  Since,  for  example,  the  tests  for 
7-year  old  children  are  too  easy,  many  less  gifted 
7-year  old  children  will  reach  the  level  of  their  age 
as  a  result  of  the  testing,  although  they  do  not  rank 
as  "satisfactory"  in  the  school.  With  the  older 
children  the  reverse  will  obtain.  Nevertheless,  I 
do  not  think  that  this  is  the  only  cause  of  the  lack  of 
agreement:  the  true  cause  lies  in  something  more 
fundamental. 

In  the  second  place,  one  might  believe  that  a  true 
picture  of  mental  endowment  was  given  only  by  the 
tests,  and  that  the  blame  for  the  disagreement 
should  be  ascribed  entirely  to  the  school;  that  the 
teachers  had  estimated  the  pupils  wrongly  when 
they  assigned  them  marks  not  in  accord  with  their 
mental  level,  and  had  treated  them  wrongly  when 
they  kept  them  back  in  a  class  beyond  which  they 
should  have  gone  according  to  their  mental  level. 
In  this  vein,  for  instance,  Goddard  writes,  for  he 
refers  this  phenomenon  almost  entirely  to  a  faulty 
system  of  promotion  (48,  pp.  241  and  249). 

But  to  dispose  of  the  matter  in  that  way  is  to 
1 '  pour  out  the  baby  with  the  bath. ' '  Of  course,  the 

"This  point  has  been  made  by  Bobertag  and  others  as  well. 


THE  METHOD  OF  AGE  GRADATION  63 

teachers,  being  human,  make  mistakes  and  not  a  few 
of  the  measures  they  adopt  may  be  based  upon  mis- 
taken judgment  of  the  mental  maturity  of  the  pupil, 
but  it  is  inconceivable  that  half  of  all  children  should 
be  victims  of  such  mistakes. 

It  seems  to  me,  rather,  that  the  results  we  have 
just  been  discussing  themselves  show  that  both  of 
the  opinions  just  cited  are  wrong.  Complete  agreed 
ment  between  school  abilitv  and  intellectual  abilit 

•/  V 

is  not  to  be  expected  at  all  nor  even  to  be  desired 
because  performance  in  the  school  depends  not  o 
upon  intelligence,  but  also  upon  certain  other  and 
quite  different  factors.  Thus,  strength  of  memory, 
which,  as  is  well  known,  is  correlated  only  to  a  mod- 
erate degree  with  intelligence,  certainly  plays  a 
large — perhaps  a  too  large — role  in  the  carrying  on 
of  school  activities  and  in  the  estimate  of  their 
worth;  the  various  special  talents,  too,  cut  across 
and  modify  the  action  of  general  intelligence.  But 
beside  this  there  are  concerned  factors  that  have 
nothing  at  all  to  do  with  intellect,  but  belong  to 
the  domain  of  will,  in  the  widest  sense  of  that  term: 
I  mean  the  degree  and  duration  of  attention,  in- 
dustry and  conscientiousness,  sense  of  duty  and 
capacity  to  fit  into  the  social  group. 

These  are  the  essential  elements  that  must  be 
added  to  intelligence  in  order  to  transform  mere 
potential  to  actual  accomplishment,  and  these  same 
elements  are  enough,  even  when  conjoined  with  in- 
tellectual ability  of  lesser  degrees,  to  produce  ef- 
ficiency of  a  worthy  degree.  This  is  true  in  life, 
and  it  is  true  also  even  in  the  school ;  and  it  is  good 
that  for  once  these  relations  should  be  brought  out 


64     PSYCHOLOGICAL   METHODS   OF  TESTING   INTELLIGENCE 

clearly  by  numerical  evidence.  For  the  figures  in 
the  tables  above  do  show  just  this,  that  intelligence 
is  never  more  than  a  partial  factor  in  school  activ- 
ity :  and  this  demonstration  may  serve  to  refute  that 
one-sided  intellectual]  sm  that  notes  and  values  in 
pupils  only  their  intellectual  ability.  Not  that  in- 
tellectual endowment  is  not  still  to  be  regarded  as 
a  factor  of  chief  importance :  in  truth  when  by  tests 
of  intelligence  and  other  psychological  devices  we 
shall  have  obtained  a  more  exact  knowledge  of  it, 
there  will  be  much  of  profit  for  the  schools  and  many 
mistakes  and  wrong  courses  of  procedure  can  be 
prevented,  and  this  so  much  the  more  as  we  get 
clear  ideas  of  the  range  and  limits  of  its  meaning 
and  importance.  If,  for  instance,  a  given  pupil 
shows  only  a  moderate  success  in  the  tests  of  intelli- 
gence but  does  distinctly  good  work  at  school,  and 
if  there  is  no  chance  that  a  special  talent  might  have 
exerted  a  decided  influence  (which  could  easily  be 
recognized  if  existent),  then  there  is  a  probability 
approximating  to  certainty  that  this  pupil's  strength 
is  to  be  sought  primarily  in  qualities  of  character 
and  will. 

Accordingly,  the  lack  of  agreement  between  tests 
of  intelligence  and  school  performance  is  really  cal- 
culated to  increase  our  confidence  in  the  psycholog- 
ical test-methods.  In  this  connection  Kramer  very 
pertinently  remarks.17  "Had  we  found  a  strict 
parallelism  between  the  results  of  the  testing  of  in- 
telligence and  the  school  performance,  we  should 


"See  reference  54,  pp.  30-31.  Kramer  was  alluding  to  the  ex- 
amination of  abnormal  children,  but  what  he  says  applies  to  nor- 
mal cases  as  well. 


THE   METHOD  OF  AGE  GRADATION  65 

have  had  to  have  felt  the  greatest  distrust  of  the 
method.  It  would  have  raised  the  suspicion  that  we 
were  doing  nothing  more  than  testing  the  school  at- 
tainments themselves,  either  directly  or  indirectly, 
in  which  event  the  method  would  be  futile  for  test- 
ing native  endowment  and  its  application  would  be 
superfluous,  for  we  would  need  only  to  resort  to  the 
school  performance  directly  for  the  information. ' ' 

(e)  Sex  differences.  Comparisons  of  the  mental 
abilities  of  boys  and  girls  have  already  been  carried 
out  in  large  numbers  in  experimental  psychology, 
but  they  have  been  almost  entirely  confined  to  single 
tests,18  whereas  the  Binet-Simon  serial  tests  have 
been  used  to  but  a  surprisingly  slight  extent  in 
the  comparison  of  the  sexes  and  have  not  yet  led  to 
positive  conclusions.  I  confine  myself  to  a  brief  ex- 
position of  the  material  in  question. 

Goddard  tested  835  boys  and  712  girls.  Unfortu- 
nately, he  has  thrown  together  the  data  for  the  dif- 
ferent ages:  it  follows  that  his  figures  (48,  p.  250) 
lose  much  of  their  value  for  comparative  purposes, 
because  retardation  and  advance  have  quite  differ- 
ent meanings  at  different  age-levels.  Nevertheless, 
we  may  reproduce  here  the  table  of  distribution  for 
the  children  (which  I  have  converted  into  percents). 

The  tabular  results  suggest  a  slight  inferiority  of 
the  boys,  most  evident  in  the  group  of  those  retarded 

18The  literature  has  been  brought  together  by  me  elsewhere 
(1:  Bibliography,  Section  VI)  ;  here  we  may  cite  the  general  sum- 
maries of  the  results  of  tests  by  Meyer  and  Wreschner,  and  the  ex- 
tensive original  studies  of  Cohn  and  Dieffenbacher  (Nos.  1048, 
1072  and  104  in  the  bibliography  just  cited).  As  one  pretty  gen- 
erally confirmed  result  may  be  mentioned,  among  others,  that  with 
the  Ebbinghaus  completion  method  girls  are  clearly  inferior  to 
boys  of  the  same  age. 


66     PSYCHOLOGICAL   METHODS  OP   TESTING   INTELLIGENCE 

one  year  to  which  23  per  cent,  of  the  boys,  but  only 
17  per  cent,  of  the  girls  belong;  the  girls  show  a 
correspondingly  greater  percentage  of  their  num- 
ber at  or  above  age. 


, Retarded (  , Advanced » 

Two  Years        One  One      Two  Years 

or  More          Year  At  Age           Year        or  More 

Boys 18.5                23  34.5                20                4 

Girls 18.5                17  36.5                23                5 

Gotidard's  statement  that  retardation  of  marked 
amount  is  more  frequent  with  boys  is  not  borne  out 
by  his  own  tables,  for  the  percentage  of  boys  and 
girls  is  here  the  same,  18.5.19 

All  the  other  investigators  that  have  treated  the 
question  of  sex  differences  have  obtained  results 
more  favorable  for  the  boys. 

Particularly  decisive  are  the  results  obtained  by 
Bloch  and  Preiss  (38)  upon  Volksschule  children  in 
the  manufacturing  city  of  Kattowitz,  in  Upper 
Silesia.  They  tested  79  boys  and  71  girls  aged  7  to 
11  years,  all  of  whom  displayed  average  native  abil- 
ity and  average  school  ability.  The  percentages 
passing  successfully  the  various  tests  show  almost 
in  every  one  of  them  a  very  decided  inferiority  of 
the  girls.  In  Table  IX  I  have  brought  together  all 
the  tests  for  which  Bloch  and  Preiss  report  the  re- 
sults separately  for  the  two  sexes.  No  particular 

"It  must,  of  course,  be  borne  in  ruiiid  that  these  are  pupils  of 
schools  for  normal  children,  but  the  statement  appears  to  be  equally 
untrue  for  abnormal  children.  From  one  of  Chotzen's  tables  (44, 
p.  462)  I  have  calculated  that  excessive  retardation,  5  years  or 
more,  appeared  in  7  of  158  feeble-minded  boys  (4.5  per  cent.),  but 
in  11  of  122  girls  (9  per  cent). 


THE  METHOD  OF  AGE  GRADATION 


67 


sex  difference  appears  in  the  description  of  pictures 
and  in  the  definition  of  abstract  terms,  and  there  is 
a  slight  superiority  of  the  girls  in  the  "hard"  prob- 
lem-questions; but  in  all  the  other  tests  the  boys 
afford  much  higher  percentages  of  success,  often 
more  than  twice  as  high.  Take,  for  instance,  the  8- 
year  old  children:  more  than  half  of  the  boys,  but 
not  a  single  girl  can  arrange  the  five  weights  cor- 
rectly; four-fifths  of  all  8-year  old  boys  recall  cor- 
rectly what  they  have  read,  solve  the  easy  problem- 
questions  and  state  correctly  the  difference  in  things 
recalled  in  memory,  whereas  the  percentage  of  girls 

TABLE   IX 
SEX  DIFFERENCES  AS   SHOWN   BY  BINET  TESTS    (BLOCH   AND  PKEISS) 


Test                                                       Age 
Description  of  Pictures 

r  7 

Memory  of  Story  Read -I      8 

I     9 
Arranging  Three  Weights 7 

f     8 

o 

Arranging  Five  Weights <    ^ 

11 
'     8 

Easy  Problem-questions \      9 

10 
'     9 

Hard  Problem-questions \    10 

11 
Defining  Abstract  Terms 

r    o 

Making  a  Sentence  with  Three  Words  |    10 

Arranging  Words  into  Sentence. ...       11 

Naming  00  Words  in  3  Minutes 

Detecting  Absurdities 11 

Comparing  Objects  from  Memory . . . .  •>      ' 


r-Percentage  of-^ 
Children  Passing 

the  Test 
Boys  Girls 

No  difference 
No  difference 
80  28 

No  difference 


73 
56 
66 
70 

77 
81 
90 
100 
25 
70 
70 


33 
0 

29 
44 
42 
55 
76 
100 
41 
80 
80 


No  difference 

70  38 

82  40 

100  100 

70  33 

76  50 

77  40 
60  50 
80  55 


68     PSYCHOLOGICAL   METHODS  OF   TESTING   INTELLIGENCE 

passing  these  tests  successfully  is  only  28,  55  and 
55,  respectively.  Where  the  same  test  runs  through 
several  years,  the  sex  difference  is  nearly  always 
greater  in  the  younger  than  in  the  older  children. 
This  corresponds,  again,  with  the  psychological  law 
that  mental  differences  stand  out  more  clearly  in 
difficult  than  in  easy  tasks. 

Bloch  and  Preiss  themselves  point  out  that  the 
number  of  persons  upon  which  these  results  are 
based  is  too  small  to  warrant  final  conclusions,  but 
it  is  surely  worthy  of  note  that  the  inferiority  of  the 
girls  extends  to  so  many  different  kinds  of  tests. 

Bobertag  (40,  II,  pp.  503-4)  compared  the  same 
number  of  boys  and  girls  of  each  age  that  ranked 
average  in  their  school  work.  In  each  age  the  mental 
age  of  the  boys  turned  out  to  be  slightly  above  that 
of  the  girls ;  the  difference  amounted  to  1/7  year  in 
the  8,  9  and  12-year  old  pupils,  and  to  1/5  year  in  the 
10  and  11-year  old  pupils. 

Mile.  Descoeudres  (46)  compared  a  very  small 
number  of  pupils — one  intelligent  and  one  unintelli- 
gent boy  and  a  like  pair  of  girls  from  each  of  six 
chronological  ages.  Taking  all  the  right  answers 
together,  the  boys  had  52,  the  girls  48  per  cent. 
There  is  here,  then,  also,  a  superiority  of  the  boys, 
though  the  amount  of  the  difference  is  not,  of  course, 
significant. 

(/)  Repeated  tests'  of  the  same  children.  Atten- 
tion must  be  called  to  one  other  important  experi- 
ment included  in  the  article  of  Bobertag 's  already 
mentioned  (40,  II) — an  experiment  that  differs  fun- 
damentally from  all  that  have  been  conducted  here- 
tofore. Bobertag  retested  in  the  year  after  a  large 


THE   METHOD  OF  AGE  GRADATION  69 

number  of  the  children  (83  in  all)  that  he  had  tested 
in  1909.  The  reapplication  of  the  same  tests  does 
not  seem  to  have  caused  any  noticeable  difficulty,  be- 
cause the  memory  of  the  details  of  the  testing  of  the 
year  before  had  as  good  as  entirely  disappeared. 
This  experiment  throws  light  upon  three  problems. 
In  the  first  place  it  sheds  an  unexpectedly  favorable 
light  upon  the  reliability  of  the  test  method.  Bober- 
tag  arranged  the  83  children  in  order  on  the  basis  of 
the  number  of  tests  solved  by  each  of  them  and 
found  that  the  order  in  the  two  years  coincided  very 
closely,  in  fact  the  correlation  amounted  to  0.95. 
Accordingly,  even  if  the  absolute  grading  into  the 
different  age-levels  of  intelligence  that  the  Binet- 
Simon  method  affords  is  still  somewhat  uncertain, 
yet  it  is  demonstrably  very  certain  in  its  relative 
gradings.  The  position  that  a  child  takes  in  a  group 
of  children  on  the  basis  of  a  single  testing  of  his  in- 
telligence may  be  deemed  to  possess  a  high  degree 
of  reliability. 

In  the  second  place  there  comes  to  light  a  clear 
relation  between  the  mental  status  of  a  child  and  the 
rate  of  his  subsequent  intellectual  development. 
Those  children  that  ranked  'at  age'  in  the  first  test- 
ing had  advanced  next  year  exactly  one  year,  on  the 
average,  while  the  retarded  children  had  advanced 
only  two-thirds  of  a  year,  and  the  advanced  children 
one  year  and  a  quarter  in  the  same  period. 

In  the  third  place  Bobertag  found  that  the  num- 
ber of  children  that  deviated,  either  above  or  below 
the  level  of  their  age,  increased  as  their  age  in- 
creased. It  follows  from  this  that,  as  chronological 
age  increases,  the  gradation  of  ages  becomes  pro- 


70     PSYCHOLOGICAL   METHODS  OP   TESTING   INTELLIGENCE} 

gressively  of  less  significance  as  a  standard  of  varia- 
tion :  an  intelligence  that  in  the  earlier  years  deviates 
above  or  below  the  level  of  its  age  by  even  less  than 
a  single  year  will  in  later  years  exceed  this  unit  of 
deviation,  which  has  then  become  relatively  smaller. 
The  same  result  had  already  been  arrived  at  in  in- 
vestigating abnormal  children,  as  will  be  shown  in 
the  following  section. 


4.    Abnormal  Children 

(a)  Mental  arrest  and  mental  retardation.  The 
mental  quotient.  When  Binet  devised  his  system  of 
tests,  he  had  particularly  in  mind  the  testing  of  ab- 
normal children  in  order  that  children  of  this  type 
could  be  recognized  opportunely  and  transferred  to 
the  special  classes  and  to  the  institutions  for  the 
feeble-minded.  Furthermore,  Binet,  together  with 
Simon,  tried  out  his  method  upon  a  large  number  of 
such  children,  though,  unfortunately,  he  has  given 
us  no  detailed  account  of  this  investigation,  but  he 
did  draw  conclusions  from  his  experiments  that 
express  the  relation  of  feeble-mindedness  to  his 
method  in  very  simple  formulas.  One  of  these 
theses  refers  to  mental  retardation  and  runs  thus 
(38,  p.  113)  :  "I  am  for  my  part  of  the  opinion  that 
every  mental  retardation  amounting  to  two  years 
can  be  regarded  as  a  serious  deficiency."  A  second 
of  these  theses  refers  to  mental  arrest  and  declares 
that  the  imbecile  does  not  progress  beyond  the 
mental  age  of  seven,  the  moron  (feeble-minded  in  the 
narrower  sense)  beyond  the  mental  age  of  nine.* 

*By  other  investigators  and  elsewhere  by  Binet  the  upper  limit 
of  moronity  is  placed  at  12  years.—  Translator. 


THE  METHOD  OP  AGE  GRADATION  71 

The  second  investigation  of  feeble-minded  chil- 
dren, that  of  Goddard  (47)  likewise  suffers  from 
lack  of  sufficiently  detailed  data.  Goddard  tested 
the  children  and  adults  in  the  Institution  for  the 
Feeble-Minded  at  Vineland,  N.  J.,  nearly  400  per- 
sons in  all,  using  the  1908  Binet  series.  He  reports, 
however,  only  the  frequency  with  which  the  several 
age-levels  were  reached  and  does  not  relate  these 
data  to  the  chronological  ages  of  his  subjects,  so  that 
it  is  quite  impossible  to  determine  the  degree  of  re- 
tardation from  his  tables.  We  can  only  derive  cer- 
tain conclusions  that  will  be  mentioned  later  on. 

The  only  thorough  investigations  that  have  thus 
far  been  made  upon  large  numbers  of  abnormal  chil- 
dren are,  accordingly,  the  tests  made  at  Breslau  by 
the  psychiatrist  Kramer  (54)  and  Chotzen  (in  con- 
junction with  Nicolauer  (43,  44)  ).  These  investiga- 
tors, by  testing  children  of  different  types,  have  sup- 
plemented each  other's  work  in  a  fortunate  manner. 
Kramer's  material  consisted  partly  of  young  per- 
sons who  had  been  brought  before  the  juvenile  court 
and  referred  thence  to  the  psychiatrist  for  expert 
opinion,  partly  of  children  that  had  visited  the 
clinics  on  account  of  mental  or  nervous  affections. 
Chotzen  applied  the  tests  in  his  capacity  of  city 
school  medical  inspector  for  special  classes:  he, 
therefore,  tested  all  the  children  that  were  newly 
turned  over  to  the  special  school  for  defectives. 
While  Kramer  had  to  do  mostly  with  older  children, 
Chotzen 's  business  led  him  to  deal  mostly  with  chil- 
dren aged  eight  and  nine  years,  but  he  extended  his 
investigation  by  including  some  of  the  older  children 
in  the  special  school.  The  technique  was  patterned 


72     PSYCHOLOGICAL   METHODS  OF  TESTING   INTELLIGENCE 

exactly  after  that  followed  by  Bobertag,  who  had 
himself  tested  a  group  of  abnormal  children  as  well 
as  normal  children. 

Both  of  these  investigators  express  a  favorable 
opinion  of  the  value  of  the  method  for  their  pur- 
poses. Thus  Kramer  writes : 

"In  summing  up  our  results  we  might  say,  first  of  all,  that  we 
are  very  much  satisfied  with  the  method  for  our  purposes.  Leav- 
ing the  quantitative  results  entirely  out  of  consideration,  we  came 
in  the  course  of  the  testing,  on  account  of  the  varied  nature  of  the 
tests,  to  get  acquainted  with  the  peculiarities  of  the  child's  make- 
up, to  understand  surprisingly  well  his  response  to  requirements  of 
a  varied  sort,  and  acquired  valuable  insight  into  the  qualitative 
differences  in  the  method  of  reaction  displayed  by  the  feeble- 
minded. In  the  case  of  the  children  sent  by  the  central  office  for 
corrective  treatment,  most  of  whom  we  could  get  hold  of  but  for  a 
single  examination,  the  relatively  short  time  that  was  needed 
(about  45  minutes  to  one  hour)  to  reach  a  reliable  judgment  con- 
cerning their  intelligence  proved  to  be  an  exceptionally  agreeable 
feature  of  the  work.  In  all  the  cases  in  which  a  judgment  con- 
cerning the  intelligence  could  be  reached  by  anamnestic  data  or  on 
the  basis  of  clinical  observations  themselves,  there  resulted  with 
but  few  exceptions  no  contradictions  with  the  outcome  of  the 
Binet  testing"  (54,  p.  27). 

To  turn,  now,  to  the  figures:  To  begin  with  the 
second  of  the  two  theses  of  Binet  that  we  cited  above, 
his  assertion  of  the  existence  of  a  "mental  arrest" 
has  also  found  confirmation  in  other  directions. 
This  thesis  may  be  stated  thus:  For  every  feeble- 
minded child  there  is  a  level  which,  once  attained, 
represents  a  definite  terminus  for  his  capacities  to 
meet  the  demands  of  mental  tests.  That  is,  even 
though  his  age  advances,  his  capacities  do  not  ad- 
vance further  than  this  level. 

Goddard  found  that  the  inmates  of  his  institution 
were  distributed  in  terms  of  mental  age  rather  uni- 
formly over  the  age-levels  from  one  to  nine  years 
(with  approximately  10  to  11  per  cent,  in  each  year), 


THE  METHOD  OP  AGE  GRADATION  73 

whereas  the  levels  10  to  12,  taken  together,  com- 
prised only  7  per  cent,  of  the  total  number.  Though 
here,  again,  he  unfortunately  put  together  those 
children  whose  age  was  such  that  they  might  per- 
haps have  been  able  later  to  transcend  the  level  in 
which  they  were  then  found  and  the  other  inmates 
whose  development  had  for  long  been  completely 
checked,  yet  his  results  do  at  least  demonstrate  that 
the  feeble-minded  only  rarely  transcend  the  mental 
age  of  nine. 

By  comparing  these  mental  ages  with  the  diag- 
noses of  the  physicians  he  arrived  at  the  following 
schema : 


/  

Imbeciles- 

\ 

Low- 

Middle- 

High- 

Type 

Idiots 

grade 

grade 

grade 

Morons 

Mental  ages  .... 

Ito2 

3  to  4 

5 

6  to  7 

8  to  12 

Goddard's  'morons'  coincide  with  our  'mentally 
feeble'  (Debilen).  The  figures  just  given  show  that 
by  far  the  greater  number  of  them  have  a  mental  age 
of  8  and  9  years. 

Kramer  (54,  p.  29)  and  Chotzen  (44,  p.  494) 
reached  similar  results. 

Goddard  compared  the  experimentally  determined 
mental  age  with  the  general  impression  that  the 
children  had  made  on  the  teachers  and  officers  of 
the  institution  and  found  a  very  satisfying  amount 
of  agreement.  The  children  of  a  given  mental  age 
formed  a  fairly  homogeneous  group,  both  in  respect 
to  their  every-day  accomplishments  and  their  ability 
to  adapt  themselves  to  the  demands  of  institutional 
life.  He  adds  to  this  a  description  of  what  can  be 
expected  in  the  line  of  practical  behavior  of  a  child 


74     PSYCHOLOGICAL   METHODS  OP  TESTING   INTELLIGENCE 

of  a  given  mental  age.  But  all  of  these  statements 
stand  very  much  in  need  of  further  testing. 

It  is  well  to  give  here  explicit  warning  against  a 
certain  false  conception  of  the  term  " arrest."  An 
ijmbecile  who,  during  his  life,  never  progresses  past 
the  mental  age  of  seven,  is  not  on  that  account  to  be 
thought  of  as  the  same  as  a  seven-year  old  child. 
/He  does  grow  beyond  that  status  in  many  respects : 
he  acquires  experiences  that  a  normal  7-year  old 
child  does  not  possess,  picks  up  many  accomplish- 
ments, experiences  the  awakening  within  himself  of 
impulses  and  needs  that  come  with  increasing  years. 
The  arrest,  then,  pertains  only  to  that  specific  group 
of  mental  abilities  that  are  tested  by  the  tests.  And 
even  some  ones  of  these  abilities  may  show  some  de- 
velopment (cf.  in  this  connection  p.  86),  only  there 
still  remain  so  many  defects  of  a  fundamental  na- 
ture that,  all  in  all,  it  is  impossible  for  him  to  rise 
above  the  mental  age  of  seven. 

Of  importance  is,  furthermore,  the  discovery  that 
Goddard  made  concerning  the  mental  age  of  a  spe- 
cial group,  the  morally  feeble-minded.  It  turned  out 
that  this  group  was  recruited  solely  from  the  upper 
of  the  age-levels  represented  in  the  institution.  Of 
22  such  individuals,  15  had  the  mental  age  9,  5  the 
age  10  and  one  each  the  ages  11  and  12.  The  circum- 
stance that  moral  defects  do  not  extend  down  be- 
yond the  mental  age  nine  is  explained  by  Goddard 
in  the  following  way:  Certain  immoral  instincts, 
i  like  the  impulse  to  lie,  to  steal,  etc.,  normally  awaken 
about  the  ninth  year;  later  on  reasoning  develops 
and  puts  these  tendencies  under  inhibition.  With 
children  whose  mental  age  is  below  nine  those  in- 


THE  METHOD  OF  AGE  GRADATION  75 

stincts  are  not  yet  developed,  whereas  with  children 
who  are  arrested  at  about  the  mental  age  of  nine, 
the  instincts  do  show  themselves  without  getting  far 
enough  along  to  develop  the  inhibition  and  so  be- 
come a  moral  defect. 

We  may  leave  undecided  the  question  of  the  cor- 
rectness of  this  explanation,  but  in  any  event  the. 
fact  remains  that  pronounced  retardation  in  moral- . 
ity  is  not  associated  with  equally  pronounced  intel-  \ 
lectual  deficiency.     The  moral  deficiency  therefore 
displays  a  certain  independence  in  its  existence,  and 
to  that  extent  the  old  designation  "moral  insanity" 
was  not  utterly  devoid  of  significance. 

We  may  allude,  also,  at  this  point,  to  a  very  sim- 
ilar conclusion  reached  by  Kramer,  who  must,  natu- 
rally, have  encountered  this  type  frequently  among 
his  criminal  subjects.  He  says:  "We  have  to  do 
here  with  individuals  whose  defectiveness  is  on  the 
moral  side  and  in  whom  there  can  be  noted  even 
from  their  early  youth  a  decided  lack  of  moral  ideas 
and  altruistic  spirit.  In  raising  the  question  as  to 
in  how  far  these  moral  defects  exist  independent  of 
intellectual  deficiency,  it  is  worth  noting  that  in  the 
examination  a  number  of  these  children  obtained  a 
result  that  corresponded  with  their  actual  age.  And  ' 
even  in  the  cases  in  which  the  mental  ability  fell  be- 
low the  norm,  there  was  no  parallelism  at  all  be- 
tween the  two  kinds  of  deficiency. '  '20 


"See  Reference  54,  p.  28.  We  may  mention  also  in  this  connec- 
tion the  results  obtained  by  Frau  Dosai-Revesz  (4)  with  separate 
tests.  She  compared  the  efficiency  in  computation,  memory  and 
report  of  normal  children,  simple  feeble-minded  and  morally  feeble- 
minded and  found  that  the  results  for  the  last-named  group  fell 
almost  entirely  between  the  results  for  the  two  other  groups. 


76     PSYCHOLOGICAL   METHODS   OF  TESTING   INTELLIGENCE 

But  this  discussion  has  already  led  us  from  the 
consideration  of  mental  arrest  to  the  question  of 
the  mental  retardation  of  the  feeble-minded.  Binet 
used  as  the  measure  of  retardation  simply  the  dif- 
ference between  mental  age  and  chronological  age 
and  was  so  convinced  of  the  general  application  of 
this  measure  that  he  looked  upon  the  value  "2 
years "  as  a  general  expression  for  a  definite  and  in 
fact  serious  deficiency. 

Binet 's  successors  also  made  use  of  this  standard, 
but  their  own  results  teach  us  that  we  can  not  be 
satisfied  with  it.  For  it  has  become  evident  that  one 
and  the  same  absolute  difference,  e.  g.f  a  mental  re- 
tardation of  three  years,  means  very  different  things 
at  different  years.  Thus  Kramer  (54)  remarks:  "It 
should  not  be  concluded  that  a  12-year  old  child  with 
a  mental  age  of  9  is  of  the  same  degree  of  feeble- 
mindedness as  an  8-year21  child  with  a  mental  age 
of  5.  In  the  case  of  the  children  turned  over  to 
us  for  examination  by  the  Central  Child  Welfare 
Bureau  (Jugendfursorgezentrale)  it  came  out  clearly 
that  the  differences  revealed  among  the  younger 
children  were  for  the  most  part  but  small,  but 
among  the  older  children  always  greater,  although 
the  actual  defects  in  these  two  groups,  so  far  as 
we  could  judge  them  by  other  criteria,  by  no  means 
revealed  any  corresponding  difference,  but  seemed, 
on  the  average,  to  be  about  the  same."  Chot- 
zen  (44,  p.  493)  also  corroborates  this  view:  "On 
account  of  a  checking  of  development,  the  mental  age 

"Page  29.  In  the  text  there  is  a  typographical  error  here,  7  in- 
stead of  8-year. 


THE   METHOD  OP  AGE  GRADATION  77 

of  feeble-minded  children  lags  progressively  more 
and  more  behind  their  chronological  age:  the 
younger  they  are,  the  more,  and  the  older  they  are, 
the  less  does  a  year's  retardation  mean  in  actual  de- 
f  ectiveness. ' ' 

How  considerable  the  fluctuations  are  may  be 
shown  by  some  figures  (Table  X)  that  I  have  de- 
rived from  one  of  Chotzen's  tables  (p.  485).  In  ad- 
dition to  the  tests,  or  rather  independently  of  them, 
Chotzen  examined  all  the  pupils  of  the  special  school 
as  the  physician  and  the  psychiatrist  ordinarily 
would,  and  classified  them,  on  the  basis  of  this  ex- 
amination, into  the  stock  groups — moron,  imbecile, 
idiot.  Some  he  had  to  class  outside  of  these  groups 
by  designating  them  as  'not  feeble-minded'  or  as 
1  doubtful  feeble-minded.'  Now,  it  might  be  sup- 
posed that  the  members  of  any  group,  e.  g.,  the 
morons,  would  necessarily  show  at  least  approxi- 
mately the  same  degree  of  mental  endowment,  re- 
gardless of  differences  in  their  chronological  ages. 
But  Table  X  shows  that  their  mental  retardation, 
computed  as  the  absolute  difference,  has  very  dif- 
ferent values  with  the  older  than  with  the  younger 
children,  and  Table  XI,  in  which  the  average  value 
of  this  measure  of  retardation  has  been  figured  for 
each  age-level,  reveals  a  rapid  increase  in  the  mag- 
nitude of  the  value,  so  that  the  12-year-old  imbeciles 
are  retarded  by  twice  as  many  years  as  the  8-year- 
old  imbeciles  (4.7  as  against  2.3  years). 

From  this  it  seems  to  me  to  follow  that  the  abso- 
lute difference  can  be  used  only  when  we  are  dealing 
with  children  of  a  given  age.  If,  for  example,  it 
should  sometime  be  arranged  to  carry  out  tests  of 


78    PSYCHOLOGICAL   METHODS  OF  TESTING  INTELLIGENCE 

intelligence  upon  all  6-year-old  children  when  they 
entered  school,  then  the  designations  ''retarded  one 
year"  or  "advanced  one  year"  would  have  an  un- 
equivocal meaning. 

TABLE   X 

FREQUENCY  OF  MENTAL  BETABDATION  IN  DIFFEBENT  FORMS  OF  FEEBLE- 
MINDEDNESS   AND    DIFFEBENT    CHBONOLOOICAL    AGES 

r— Not  Feeble-minded-^  ,— Doubtfully  Defective— >> 

Retardation 0  1  Yr.  2  Yrs.  3  Yrs.  1  Yr.  2  Yrs.  3  Yrs.  4  Yrs. 

8    6    11                •  /  13          4 

975  13 


Chronological 
Age ' 


10  2  3 

11  1  1 

12  1  1 

13  1 


/ Morons ^     , Imbeciles * 

1234  12345 

Retardation Yr.  Yrs.  Yrs.  Yrs.  Yr.  Yrs.  Yrs.  Yrs.  Yrs. 

84       10      2        ,«  6     21        9       2        1 

Chronological            9              15      2  8     30       8       2 

10                57  ,                    754 

Age 11                       5         1  2 

12                       21  12 

But  it  is  another  matter  when  we  have  to  consider 
children  of  quite  different  ages  or  when  we  want  to 
express  the  degree  of  backwardness  in  a  formula  of 
general  validity.  The  value  based  on  absolute  dif- 
ference, if  given  by  itself,  may  mean  very  different 
things,  so  that  at  least  the  chronological  age  ought 
always  to  be  stated  to  enable  the  reader  to  figure  out 
the  degree  of  importance  to  be  attached  to  the  dif- 
ference. To  what  prolixity  of  statement  this 
method  leads  one  may  be  illustrated  by  the  follow- 
ing sentence  from  Chotzen  (pp.  493-4):  "Children 
of  8  to  9  years  can  suffer  a  deficiency  of  one  year, 
those  of  10  to  12  years  one  of  two  years  without 


THE  METHOD  OF  AGE  GRADATION  79 

feeble-mindedness  being  present,  but  a  backwardness 
of  two,  or  of  three  years,  respectively,  for  these  ages, 
certainly  cannot  coexist  with  normal  intelligence." 

TABLE  XI 
AVERAGE  RETARDATION,  IN  YEARS,  OF  THE  CHILDREN  IN  TABLE  X 

Chronological         Not  Doubtful 

Age         Feeble-minded  Defect  Morons  Imbeciles 

8  0.65  1.3                     1.9                       2.3 

9  1.4  1.7                    2.1                       3.1 

10  2.0  2.0  2.6  3.8 

11  3.0  3.5  3.2  4.0 

12  2.0  3.0  3.3  4.7 

13  3.5 

That  the  size  of  the  absolute  difference  for  the 
same  degree  of  feeble-mindedness  should  increase 
as  age  increases  is  psychologically  easily  intelligible, 
for,  since  feeble-mindedness  consists  essentially  in 
a  condition  of  development  that  is  below  the  normal 
condition,  the  rate  of  development  will  also  be  a 
slower  one,  and  thus  every  added  year  of  age  must 
magnify  the  difference  in  question,  at  least  as  long 
as  there  is  present  anything  that  could  be  called 
mental  development  at  all.  With  this  in  mind  it  is 
but  a  step  to  the  idea  of  measuring  the  backward- 
ness by  the  relative  difference,  i.  e.,  by  the  ratio  be- 
tween mental  and  chronological  age,  instead  of  by 
the  absolute  difference.  Bobertag  had  already  con- 
ceived a  plan  of  this  sort,  while  Kramer  (54,  p.  30) 
hints  at  something  of  the  sort,  though  very  guard- 
edly: "Whether  perhaps  there  might  be  devised  a 
specific  method  of  calculation  for  relating  the  dif- 
ference in  years  to  chronological  age  and  which 
would  then  give  us  an  absolute  measure  for  degree 
of  feeble-mindedness,  seems  to  me  a  matter  of 
doubt." 


80     PSYCHOLOGICAL   METHODS   OP   TESTING   INTELLIGENCE 

The  results  of  Chotzen  that  now  lie  before  us  per- 
mit us  to  test  the  feasibility  of  a  relative  measure  of 
this  sort.  I  should  like  to  recommend  the  relating 
to  chronological  age  not  of  the  difference,  but  of  the 
mental  age  itself.  We  would  then  obtain  the  mental 
quotient  that  has  already  been  mentioned  (p.  42). 
This  quotient  shoivs  what  fractional  part  of  the  in- 
telligence normal  to  his  age  a  feeble-minded  child 
attains.  Mental  quotient  =  mental  age  -r-  chrono- 
logical age.  An  8-year  old  child  with  a  mental  age 
of  six  has,  then,  a  mental  quotient  of  6/8  —  0.75.  A 
12-year  old  child  with  a  mental  age  of  9  has  the  same 
mental  quotient. 

TABLE   XII 
AVERAGE   MENTAL  QUOTIENT  OF  THE  CHILDBEN  IN  TABLES  X  AND  XI 

Chronological         Not  Doubtful 

Age         Feeble-minded     Defect  Morons  Imbeciles 

8  0.92  0.84  0.76  0.71 

9  0.85  0.81  0.77  0.67 

10  (0.80)  (0.80)  0.74  0.62  . 

11  (0.73)  (0.68)  0.71  (0.64) 

12  (0.75)  (0.75)  (0.73)  (0.61) 

13  (0.73) 

Now  when  we  turn  into  quotients  the  values  cal- 
culated from  Chotzen  in  Table  XI,  we  obtain  Table 
XII.  The  idiots  have  been  omitted  for  reasons  that 
will  appear  later.  The  figures  in  brackets  are  those 
that  cannot  be  deemed  reliable  averages  on  account 
of  too  few  individuals  included  in  them.  The  table 
reveals  mental  quotients  for  the  two  main  forms  of 
feeble-mindedness  that  are,  it  is  true,  not  constant, 
but  that  are,  however,  very  similar  through  several 
chronological  years.  The  morons,  in  especial,  show 
surprisingly  uniform  values ;  their  average  quotient 


THE   METHOD  OF  AGE  GRADATION  81 

varies  only  within  the  narrow  range  0.71  to  0.77  for 
the  five  years  8  to  12.  Roughly  expressed,  therefore, 
their  intelligence,  measured  by  that  of  normal  per- 
sons, is  a  'three-quarter  intelligence.'  The  imbeciles 
show  somewhat  greater  variations,  but  their  mental 
quotients  are  in  quite  fair  agreement,  at  least  for 
the  years  9  to  11.  They  entitle  their  possessors, 
again  roughly  speaking,  to  a  scant  'two-thirds  intel- 
ligence. ' 

The  first  two  of  Chotzen's  groups  are  represented 
by  too  few  cases  to  permit  consideration  of  their 
averages,  save  at  most  for  the  younger  ages.  In 
these  ages  the  mental  quotient  agrees  finely  with  the 
medical  diagnosis  of  the  children.  Those  desig- 
nated as  "not  feeble-minded"  have  a  mental  quotient 
of  about  0.90,  while  the  doubtfully-defective,  whose 
quotient  lies  between  0.80  and  0.84,  form  a  real  in- 
termediate grade  between  the  'not-abnormal'  and 
the  true  morons.  The  isolated  cases  of  older  chil- 
dren (7  in  all)  that  Chotzen  classified  in  these  two 
groups,  are  ranked  by  their  quotient  largely  in  the 
morons.  It  is  possible  that  the  mental  quotient  may 
supplement  uncertain  medical  diagnoses  in  cases  of 
this  sort. 

Now  the  objection  might  be  raised  to  the  above 
series  of  quotients  that  they  comprise  only  averages 
and  that  these  have  been  derived  in  part  from  a  too 
small  number  of  values.  To  meet  this  objection  I 
have  made  another  computation  in  which  I  have 
worked  out  the  mental  quotients  of  individual  chil- 
dren, and  then  have  recorded  their  frequency-dis- 
tribution. In  this  computation  I  have  disregarded 
chronological  age,  and  have  combined  in  each  case 


82     PSYCHOLOGICAL    METHODS  OF  TESTING   INTELLIGENCE 


the  values  for  10  points  on  the  scale,  e.  g.,  the  quo- 
tients lying  between  1.00  and  91,  between  0.81  and 
0.90,  etc. 

TABLE  XIII 
DISTBIBUTION    OF    MENTAL    QUOTIENTS    IN    DIFFEBENT    GROUPS    OF 


FEEBLE-MINDED 


Not 

Mental 

Feeble-Md'd 

r-Doubtful- 

Quotient 

Abs. 

Rel. 

Abs. 

Rel. 

0.91-1.00... 

.     6 

18 

0.81-0.90.  .  . 

.  19 

57 

14 

48 

0.71-0.80... 

.     8 

25 

13 

45 

0.61-0.70.  .  . 

. 

2 

7 

0.51-0.60.  .  . 

t 

0.41-0.50... 

, 

0.31-0.40... 

, 

Abs.      Rel. 


<—  Imbeciles— •> 
Abs.       Rel. 


Totals...   33 


100 


100 


5 
37 
13 


55 


9 
67 
24 


100 


6 

30 

49 

15 

9 

2 

111 


5.5 
27. 
44. 
13.5 

8 

2 

100 


Table  XIII  shows  the  distribution  of  the  results 
obtained  in  this  way,  both  in  absolute  numbers  and 
in  percentages :  Figure  1  also  shows  the  distribution 
of  the  percentages  graphically. 


FIG.  i. 


DISTRIBUTION  OF  MENTAL  QUOTIENTS  DERIVED  FROM 
CHOTZEN'S  RESULTS. 

=  not  feeble-minded. 

=  doubtful. 

— . — . — . — . — . — .  =  moron. 
=  imbecile. 


THE  METHOD  OF  AGE  GRADATION  83 

There  appears  a  clear  separation  of  the  points  of 
maximal  frequency  for  the  chief  groups,  and,  it  is 
to  be  noted,  the  mental  quotient  of  the  'not-abnormal' 
children  lies  mostly  between  0.81  and  0.90,  that  of 
the  morons  between  0.71  and  0.80,  that  of  the  im- 
beciles between  0.61  and  0.70 — all  quite  in  accord- 
ance with  our  earlier  figures.  In  the  case  of  the  im- 
beciles the  range  of  the  quotients  is  wider  than  with 
the  other  groups,  as  the  average  values  had  already 
shown.  Attention  should  be  called  to  the  fairly 
symmetrical  form  of  the  three  curves :  this  brings  it 
about  that  the  point  of  maximal  frequency  and  the 
average  tend  to  coincide  within  each  group. 

The  transitional  character  of  the  group  of  doubt- 
fully defective  also  finds  expression  typically  in  that 
its  members  are  distributed  fairly  uniformly  over 
the  regions  that  are  characteristic  on  the  one  hand 
of  the  normals  and  on  the  other  hand  of  the  un- 
doubted morons. 

The  number  of  the  children  tested  by  Chotzen  is 
not  yet  large  enough  and  particularly  their  distri- 
bution over  the  different  age-levels  is  not  wide 
enough  to  consider  the  above  figures  as  having  con- 
clusive value  for  other  sets  of  material,  yet  they  do 
seem  to  me  so  far  removed  from  objection  as  to 
demonstrate  that  the  mental  quotient  is  a  very  much 
more  useful  measure  of  backwardness  than  the  com- 
monly used  absolute  difference. 

The  quotient  does  not  seem,  however,  to  afford  an 
actually  constant  expression  of  degree  of  feeble- 
mindedness, but  shows  a  tendency  to  fall  in  value  as 
age  increases.  This  tendency,  it  is  evident,  is  but 
plight  within  the  limits  of  age  that  have  been  men- 


84     PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

tioned,  so  that  for  many  problems  it  can  be  neglected. 
Before  and  after  these  ages  the  fall  in  the  value 
seems  to  take  place  more  rapidly.  In  the  case  of  the 
later  age-levels  this  is  easily  intelligible,  for  once 
the  stage  of  arrest  that  we  have  previously  dis- 
cussed is  reached  (for  morons  at  the  mental  age  of 
9),  the  quotient  obtained  by  dividing  mental  by 
chronological  age  must  decrease  as  chronological 
age  increases.  The  feeble-minded  child,  it  must  be 
remembered,  not  only  has  a  slower  rate  of  develop- 
ment than  the  normal  child,  but  also  reaches  a  stage 
of  arrest  at  an  age  when  the  normal  child's  intelli- 
gence is  still  pushing  forward  in  its  development. 
At  this  time,  then,  the  cleft  between  the  two  will  be 
markedly  widened. 

From  these  considerations  it  follows  that  the 
mental  quotient  can  hold  good  as  an  index  of  feeble- 
mindedness only  during  that  period  when  the  de- 
velopment of  the  feeble-minded  individual  is  still  in 
progress.  It  is  for  this  reason  that  there  is  no  sense 
in  calculating  the  quotient  for  idiots,  because,  in 
their  case,  the  stage  of  arrested  development  has 
been  entered  upon  long  before  the  ages  at  which 
they  are  being  subjected  to  examination.  The  above- 
mentioned  gradual  tendency  of  the  mental  quotient 
to  sink  during  the  progress  of  development  shows 
that  this  development  approaches  the  final  level  of 
arrest  at  a  progressively  decreasing  rate.22 

Whether  we  shall  succeed  some  time  in  finding  a 
formula  for  a  truely  constant  coefficient  of  feeble- 
mindedness must  be  left  for  the  future. 


""In  his  last  article  (40,  II)  Bobertag  lays  special  stress  on  this 
progressive  retardation  in  the  rate  of  development  of  the  feeble- 
minded and  attempts  to  present  it  in  graphic  form. 


THE   METHOD  OP  AGE  GRADATION  85 

(b)  Relation  to  the  several  tests.  It  must  not  be 
thought  that  the  significance  of  the  Binet- Simon 
method  for  the  study  of  feeble-mindedness  is  re- 
stricted to  the  possibility  of  grading  them  quanti- 
tatively. Perhaps  even  more  important  than  this 
is  the  qualitative  analysis  of  the  individual  subject 
that  the  method  allows  and  the  discovery  of  how  the 
several  tests  have  participated  in  the  final  values. 
Chotzen  's  investigation,  the  first  to  attack  this  prob- 
lem, has  shown  how  confusingly  many  special  prob- 
lems and  matters  of  interest  are  to  be  unearthed  in 
this  field. 

At  the  very  outset,  for  example,  there  is  thrust 
insistently  upon  us  the  question :  Have  we  any  right 
at  all  to  equate  a  10-year-old  feeble-minded  child 
with  a  7-year-old  normal  child  just  because  the  re- 
sult of  testing  gives  him  a  mental  age  of  7  years: 
in  other  words,  can  we  say  that  feeble-mindedness 
is  actually  mere  'backwardness.'  It  is,  indeed,  quite 
often  asserted  that  this  expression  is  misleading 
because  feeble-mindedness  is  something  qualita- 
tively different  from  normality.  But  the  Binet- 
Simon  method  makes  it  possible  for  us  to  work  out 
the  comparison  between  the  two  mental  conditions 
exactly. 

And  in  fact  comparison  does  show  that  the  mental 
age  of  7  years  is  not  reached  in  the  tests  in  quite  the 
same  way  that  the  normal  7-year-old  child  reaches 
the  same  mental  age,  for  the  area  of  irregular  dis- 
tribution is  very  much  wider  with  the  feeble-minded 
than  with  the  normal  child.  Bobertag,  in  an  as  yet 
unpublished  discussion,  reckons  the  distribution  at 
twice  the  area  of  that  of  a  normal  child.  In  other 


86     PSYCHOLOGICAL   METHODS  OF   TESTING   INTELLIGENCE 

words  we  may  say  that  the  'hits'  and  'misses'  of  the 
older  feeble-minded  children  are  scattered  over  very 
many  more  age-levels  than  are  those  of  younger 
normal  children :  the  defective  fails  unexpectedly  to 
pass  some  quite  easy  tests,  but  succeeds  here  and 
there  in  meeting  much  higher  requirements.  There 
appears  a  certain  dissociation  of  abilities  that  are 
normally  more  strictly  intercorrelated. 

We  are  now  in  a  position,  moreover,  to  discover 
general  principle  obtaining  in  this  dissociation. 
'here  are  certain  abilities  that  are  essentially  a 
function  of  age,  relatively  independent  of  intelli- 
gence: there  are  other  abilities  that  are  conditioned 
entirely  by  specific  degrees  of  intellectual  develop- 
ment, regardless  of  the  age  at  which  this  develop- 
ment is  attained.  A  child  of  9  or  10  years  of  age, 
even  if  he  be  defective,  will  be  farther  advanced  than 
a  normal  child  of  6  or  7  years  of  age  in  abilities  of 
the  first  sort;  but  a  normal  child  necessarily  sur- 
passes a  feeble-minded  child  in  abilities  of  the  second 
sort. 

A  priori  we  should  expect  that  to  the  first  sort  of 
abilities  (those  conditioned  by  age)  would  belong 
those  dependent  upon  a  mass  of  experiences  fre- 
quently had  and  activities  frequently  discharged  in 
everyday  life.  But  a  priori  opinions  of  this  sort  are 
of  no  great  service  to  us,  and  it  will  be  of  corre- 
spondingly great  value  for  us  to  be  able  to  discover 
by  an  analysis  of  the  results  of  Binet-Simon  tests 
which  of  the  tests  applied  to  the  feeble-minded  cor- 
relate more  with  age  and  which  more  with  real  in- 
telligence. Up  to  now  the  results  of  Chotzen  are 
alone  available  for  this  purpose  and  even  they  af- 


THE   METHOD  OF  AGE  GRADATION  87 

ford  but  an  incomplete  survey  because  Chotzen  had 
to  deal  almost  entirely  with  feeble-minded  children 
of  a  single  age-group  (8  to  9  years). 

Chotzen  gives  us  a  whole  series  of  computations 
to  show  the  worth  of  the  different  tests  for  the  diag- 
nosis of  f eeble-mindedness :  the  perusal  of  his  diffi- 
cult exposition  will  afford  the  reader  a  new  idea  of 
the  complications  that  arise  when  one  really  tries  to 
analyze  the  serial  system  of  tests  to  the  last  details. 
Because  a  repetition  of  investigations  of  this  sort, 
especially  with  feeble-minded  children  of  more  ad- 
vanced ages  is  very  much  to  be  desired,  we  feel  war- 
ranted in  introducing  here  a  brief  account  of  the 
methods  that  Chotzen  pursued  in  evaluating  the 
tests. 

The  simplest  thing  is,  of  course,  the  direct  com- 
parison of  feeble-minded  with  normal  children  of 
the  same  age  (using  Bobertag's  data). 

From  such  a  comparison  it  appeared  (44,  p.  440)  that  the  back- 
wardness of  the  feeble-minded  was  least  in  the  following  tests: 
telling  forenoon  from  afternoon,  defining  in  terms  of  use,  knowing 
own  age,  esthetic  judgment,  telling  the  number  of  the  fingers, 
describing  a  picture,  counting  13  pennies ;  the  backwardness  was, 
on  the  other  hand,  very  pronounced  in  the  following:  memory-span 
for  16  syllables  and  for  5  digits,  making  change  (80  Pfennige  for 
1  Mark),  counting  backward  from  20  to  0,  definition  by  super- 
ordinate  terms,  comparison  of  two  objects  from  memory,  recall  of 
a  short  story,  naming  the  months  and  arranging  the  five  weights. 

With  children  of  other  ages  these  lists  would  pre- 
sumably change.  Thus  the  explanation  of  the  pic- 
ture which  is  demanded  of  older  children  would 
doubtless  bring  out  a  decided  difference  between 
normal  and  feeble-minded  children,  though  the  de- 
scription of  the  picture  which  is  demanded  of  the 
younger  children  did  not  bring  out  such  a  difference, 
according  to  Chotzen. 


88    PSYCHOLOGICAL  METHODS  OP  TESTING   INTELLIGENCE 

However,  even  these  lists  of  Chotzen's  suffice  to 
show  that  the  differences  between  the  two  types  of 
children  turn  out  to  be  small  in  those  tests  that  re- 
late to  frequently  practiced  activities  (counting,  tell- 
ing how  old  they  are)  and  to  common  experiences  of 
everyday  life  (number  of  fingers,  forenoon  and 
afternoon) ;  on  the  other  hand,  the  deficiency  of  the 
/feeble-minded  is  at  once  revealed  in  its  entirety 
/the  moment  that  something  unusual  is  demanded, 
/  that  something  new  is  presented  and  that  attention 
must  be  sharply  concentrated. 

A  similar  comparison  can  be  carried  out,  in  the 
next  place,  amongst  the  special-class  pupils  them- 
selves, i.  e.,  between  the  different  groups  of  feeble- 
minded that  the  medical  diagnosis  had  established: 
Chotzen  found  out  which  tests  exhibited  a  specially 
decided  drop  from  one  group  to  another  in  the 
feeble-minded  children  of  the  same  age.  I  mention 
only  those  that  showed  a  clear  falling  off  of  one-half 
in  passing  from  the  ''not  feeble-minded"  to  the 
morons  and  from  the  morons  to  the  imbeciles. 

For  8-  and  9-year-old  children :  drawing  a  diamond,  repeating 
five  digits,  easy  problem-questions.  There  was  a  somewhat  smaller 
falling  off  in  counting  five  coins  and  comparing  two  objects. 

For  older  children  (Chotzen  had  also  tested  a  series  of  older 
children  for  purposes  of  comparison)  :  comparison,  reproduction  of 
the  item  in  the  newspaper,  arranging  five  weights,  making  change, 
defining  by  superordinate  terms,  knowing  various  pieces  of  money, 
repeating  five  digits. 

Thirdly  and  lastly,  Chotzen  figured  out  compara- 
tive results  for  those  subjects  of  the  same  mental, 
but  of  different  chronological  age,  as  might  happen, 
for  instance,  if  an  8-year-old  child  were  retarded 
two  years,  a  9-year-old  child  three  years,  or  a  10- 


THE  METHOD  OF  AGE  GRADATION  89 

year  old  child  four  years.  He  found  that  when 
children  of  a  single  mental  level  were  considered, 
some  tests  show  a  clear  increase  in  capacity  with  in- 
crease in  chronological  age,  others  no  alteration, 
while  yet  others  an  actual  decrease.  Tests  of  the 
first  sort,  those  that  have  an  'age-increase,'  are 
doubtless  tests  that  have  least  to  do  with  intelli- 
gence, because,  given  the  same  intelligence,  they  are 
nevertheless  better  done  by  the  older  children.  On 
the  contrary,  the  other  tests  plainly  stand  in  correla- 
tion with  intelligence,  more  particularly  the  tests  in 
which  the  older  children  actually  turn  out  poorer. 
The  following  are  the  results : 

Decided  increase  with  age  is  shown  in  copying,  writing  from 
dictation,  the  recall  of  two  items  of  a  story,  naming  the  days  of 
the  week. 

"The  tests  accompanied  by  strong  increase  with  age  relate,  then, 
almost  exclusively  to  matters  of  information,  particularly  of 
school-information,  the  assimilation  of  which  depends  on  the  ex- 
tent of  instruction.  Where  only  a  slight  increase  is  to  be  detected, 
information  also  plays  a  r61e  in  some  of  the  tests  (five  coins, 
knowing  age),  but  for  the  most  part  the  tests  are  such  that  not 
only  practise,  but  also  the  natural  increase  of  efficiency  will  im- 
prove the  results,  e.  g.,  execution  of  three  orders,  counting  back- 
wards, repeating  16  syllables.  In  all  of  these  the  increase  with 
age  is  slight.  No  increase  at  all  is  present  with  tests  that  demand 
ability  to  judge  and  to  combine  or  with  such  as  put  severe  de- 
mands upon  apprehension — comparison,  problem-questions,  noting 
omissions,  repeating  five  digits"  (44,  p.  453). 

To  this  last  category  probably  belong  also:  recall  of  six  details 
of  a  story,  arrangement  of  the  five  weights,  explanation  of  a  pic- 
ture, making  change,  though  the  figures  are  too  small  in  these  cases 
to  permit  positive  conclusions. 

When  we  compare  with  each  other  these  different 
lists  obtained  in  different  ways,  we  note,  it  is  true, 
deviations  in  many  details,  yet,  taken  as  a  whole,  the 
same  tests  keep  cropping  up  as  the  ones  in  which 
defective  intelligence  is  laid  bare,  unconcealed  and 


90    PSYCHOLOGICAL   METHODS  OP  TESTING   INTELLIGENCE 

uncompensated,  while  in  the  other  tests  the  defect  of 
intelligence  can  be  made  good  by  greater  age. 

When  investigations  of  this  kind  shall  have  been 
carried  out  with  a  large  number  of  feeble-minded 
individuals  of  different  chronological  ages,  we  may 
hope  to  reach  a  far  deeper  insight  into  the  whole 
structure  of  defective  intelligence  in  its  different 
stages  of  development  and  degrees  of  enfeeblement. 

(c)  Intelligence  and  school  ability.  The  problem 
we  have  already  met  with  the  normal  children  (pp. 
57  ff.)  meets  us  again  with  the  abnormal  and  leads 
us  to  quite  similar  conclusions.  That  is,  only  a  par- 
tial correspondence  exists  between  the  magnitude 
of  the  mental  defect  and  the  reduction  in  school 
ability.  Kramer  states  that  a  large  number  of  chil- 
dren were  retarded  in  their  school  classes  by  the 
same  number  of  years  as  they  were  retarded  in  in- 
telligence, yet  there  were  a  good  many  who  were 
more  backward  in  school  status  than  in  intelligence 
(the  opposite  condition,  less  backward  in  the  school, 
almost  never  obtained).  In  fact,  there  were  some 
children  completely  incompetent  for  school  work  in 
whom  no  corresponding  mental  defect  could  be  made 
out. 

Similarly,  among  the  8-  and  9-year-old  children 
turned  over  to  the  special  classes  (auxiliary  school) 
Chotzen  found  a  large  number  that  did  not  have  the 
two  years  of  backwardness  demanded  by  Binet  for 
such  a  condition,  but  who,  nevertheless,  certainly 
belonged  in  the  special  school,  because  they  failed 
completely  in  the  regular  school. 

This  pedagogical  retardation  that  is  non-intel- 
lectually  conditioned  is,  as  will  be  understood,  in 


THE  METHOD  OF  AGE  GRADATION  91 

some  cases  a  product  of  external  conditions,  in  par- 
ticular of  poor  home  conditions,  neglect,  change  of 
residence  and  school,  long  illness,  etc.  In  other 
cases,  however,  what  is  lacking  is  something  in- 
ternal: those  volitional  attributes  that  must  supple- 
ment intelligence  to  produce  useful  men  are  not  de- 
veloped to  the  same  degree  as  the  intelligence. 
There  are,  then,  the  morally  feeble-minded:  "chil- 
dren of  this  type,  as  one  might  expect,  shirk  their 
lessons,  are  up  to  all  sorts  of  mischief  in  the  class, 
are  quite  unaffected  by  punishments,  and  so  forth, 
so  that,  despite  good  intelligence,  they  more  or  less 
often  fail  of  promotion.  Those  cases  in  which  these 
mental  anomalies  are  accompanied  by  intellectual 
deficiency  of  a  small  degree  prove  to  be  especially 
unpropitious  (Kramer,  54,  p.  31). 

5.    Points  of  View  for  the  Reorganization  and  Im- 
provement of  the  Gradation  Method 

Our  discussion  has  revealed  already  a  series  of 
more  or  less  serious  defects  in  the  Binet-Simon 
method,  nor  have  these  defects  been  removed  by  the 
revision  made  by  Binet  himself  in  1911.  Nearly 
every  user  of  the  method  has  called  attention  to 
weaknesses  of  some  sort  in  it;  moreover,  many  do 
more  than  merely  criticize ;  they  make  proposals  for 
modifying  or  supplementing  the  method,  or  even 
make  use  themselves  without  more  ado  of  modified 
methods  of  conducting  the  tests  at  this  or  that  point. 

But  it  would  become  a  very  serious  matter  if  in- 
dividual investigators,  on  mere  grounds  of  personal 
preference  or  chance  bits  of  criticism,  should  be  for- 
ever making  changes  in  an  instrument  of  investiga- 


92     PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

tion  that  has  attained  international  usage ;  on  the  one 
hand  such  tinkering  will  destroy  the  balance  of  the 
whole  system  in  which  every  test  is  peculiarly  bound 
up  with  every  other  test,  and  on  the  other  hand  it 
will  put  an  end  to  the  comparison  of  the  results  of 
different  investigators. 

For  these  reasons  it  is  to  be  recommended  that 
we  proceed  in  the  future  in  this  way:  wherever  our 
object  is  to  lay  the  emphasis  on  the  substance  of  the 
results  secured,  as  in  the  testing  of  children  for 
practical  purposes,  let  us  for  the  present  still  con- 
tinue to  use  the  old  system,  despite  its  evident  de- 
fects. But  independently  from  this,  let  investiga- 
tions directed  to  methodological  issues  be  under- 
taken ivith  the  aim  of  constructing  a  gradation  sys- 
tem that  shall  be  revised  in  every  particular.  But 
this  task  is  beyond  the  ability  of  the  individual  in- 
vestigator :  the  problems  to  be  solved  are  too  many 
and  varied  and  the  number  of  individuals  that  should 
be  tested  is  too  great.  Bather  is  it  true  that  here,  if 
anywhere,  is  there  opportunity  for  that  community 
and  division  of  work  that  is  everywhere  now  de- 
manded in  psychology. 

To  prepare  the  way  for  the  carrying  out  of  such  a 
program  I  enumerate  here  the  chief  points  to  be 
considered  in  this  work  of  reconstruction  and  also 
offer  for  discussion  some  specific  proposals  of  my 
own  for  modifications  in  the  system. 

(a)  Selection  and  appraisement  of  the  various 
tests.  The  criticism  that  has  been  passed  upon  the 
various  tests  has  been  based  sometimes  on  theoreti- 
cal considerations,  sometimes  on  practical  results. 
The  critique  of  Ayres  (31),  who  has  done  no  work 


THE  METHOD  OF  AGE  GRADATION  93 

/himself  with  the  method,  is  an  instance  of  the  first 
[type.  He  complains  that  the  tests  have  too  seldom 
\a  direct  relation  to  practical  intelligence,  that  they 
principally  concern  such  things  as  fluent  use  of  lan- 
guage, memory  span,  response  to  problem  questions 
that  are  quite  foreign  to  real  life,  and  also  in  part 
attainments  that  are  to  a  great  degree  dependent 
on  instruction  and  on  influences  of  the  home  environ- 
ment, and  also  work  with  abstract  concepts — some- 
tiling,  he  says,  with  which  only  philosophers  have  to 
deal  ( !),  whereas  they  do  not  touch  the  ability  to  get 
on  with  the  activities  of  life;  he  wants  more  "doing 
tests"  introduced.  Although  Ayres'  criticism  is  jus- 
tified in  many  respects,  yet  he  seems  to  have  over- 
looked the  fundamental  fact  that  intelligence  is  a 
formal  activity,  and  that  of  necessity  it  is  operative 
also  in  tasks  whose  content  is  not  such  as  appears  in  i 
real  life.  Indeed,  problems  of  this  sort  have  the 
methodological  advantage  that  there  is  certainly  no 
uncontrollable  influence  of  training  in  them. 

More  important  are  the  criticisms  that  proceed 
from  the  empirical  retrial  of  the  tests.  It  has  been 
shown  that,  as  a  matter  of  fact,  there  is  too  inti- 
mate dependence  with  school  and  environmental  in- 
fluences in  many  of  the  tests ;  others  could  not  be  as- 
signed positively  to  a  specific  age-level  or  showed 
no  clear  differences  in  the  performances  of  children 
of  unmistakably  different  intelligence.  Again,  objec- 
tion is  to  be  raised  to  those  tests  in  which  there  is  a 
strong  probability  that  the  right  answer  may  be  a 
matter  of  mere  chance,  like  the  tests:  "Show  me 
your  right  hand,  your  left  ear"  and  "Is  it  forenoon 
or  afternoon  1 ' ' 


94     PSYCHOLOGICAL    METHODS  OF   TESTING   INTELLIGENCE 

The  fitness  of  a  test  to  be  employed  at  all,  and  its 
assignment  to  a  given  age-level  is  something  that  we 
shall  be  able  in  the  future  to  work  out  by  different 
methods. 

In  the  first  place  we  have  to  make  use  of  the  rela- 
tion between  the  age-level  and  the  test.  In  general,  • 
for  a  test  to  be  valid  for  a  certain  level,  the  require- 
ment is  that  approximately  75  per  cent,  of  all  chil-  \ 
dren  of  this  age  shall  be  able  to  pass  the  test.  This 
requirement  would  correspond  to  the  normal  stand- 
ard of  validity  previously  mentioned  (p.  45  f.),  and 
Bobertag,  as  more  recently  Bell  (32),  has  actually 
checked  up  the  assignment  of  given  tests  to  given 
age-levels  in  accordance  with  this  principle ;  Terman 
and  Childs  (63)  take  66  per  cent,  for  the  critical 
value,  though  this  would  seem,  for  the  reasons  al- 
ready cited,  to  be  less  appropriate. 

Taken  alone,  however,  this  principle  is  inadequate, 
for  it  does  not  inform  us  whether  the  test  would  be 
characteristic  for  just  this  age-level  only  and  not 
just  as  much  or  nearly  as  much  for  another  age-level. 
To  determine  this  we  must  discover  with  what  fre- 
quency the  test  is  passed  in  other  ages;  and  that 
test  is  most  useful  that  shows  the  most  decided  ad- 
vance with  age  (a  helpful  methodological  device  to 
which  Bobertag  was  the  first  to  call  attention). 

For  the  sake  of  illustration  let  us  invent  an  example.  Suppose 
two  tests  have  each  been  passed  successfully  by  75  per  cent,  of 
9-year-old  children,  but  that  the  one  test  shows  little,  the  other 
decided  difference  in  the  frequency  with  which  it  is  passed  by 
8-  and  10-year  old  children.  If  Test  A  be  passed  by  65,  75  ami  ou 
per  cent,  of  8-,  9-  and  10-year  old  children,  respectively,  and  Test  B 
by  45,  75  and  90  per  cent,  in  the  same  three  ages,  respectively,  then 
the  latter  test  sets  a  task  whose  performance  is  just  normal  for 
the  9-year-old,  as  compared  with  the  8-year-old  children,  and  prac- 
tically a  self-evident  activity  for  10-year-old  children;  Test  B  is 
then  the  more  useful  test 


THE   METHOD  OF  AGE  GRADATION  95 

Since  the  process  of  mental  development  brings 
into  maturity  in  succession  a  series  of  different  part- 
functions,  it  follows  that  for  each  age  there  should 
be  a  series  of  tests  to  correspond  to  the  phenomena 
of  development  that  have  just  appeared ;  it  must  be 
possible,  with  the  aid  of  the  principle  of  decided  ad- 
vance with  age,  to  pick  these  tests  out  from  a  num- 
ber of  others. 

Again,  the  matter  of  correspondence  between  the 
results  of  different  investigations  must  be  consid- 
ered in  the  selection  of  the  tests.  A  test  that  grades 
the  same  or  nearly  the  same  with  German,  French, 
English  and  American  children  has  naturally  more 
claim  to  be  included  in  the  final  system  than  one  that 
varies  markedly  with  the  examiner  or  with  the  ex- 
aminees. The  table  that  Bell  (32)  has  prepared  is 
instructive  in  this  connection.  He  presents,  side  by 
side,  the  age-rank  that  each  of  the  Bmet-Simon 
tests  would  have  attained  on  the  basis  of  the  results 
of  Binet,  Levistre  and  Morle,  Johnstone,  Goddard, 
Bobertag,  and  Terinan  and  Childs.23 

In  many  of  the  tests  the  variations  are  quite  large;  thus,  the 
test  of  "comparing  two  objects  from  memory"  ranges  from  the  6th 
year  (Johnstone)  to  the  9th  year  (Terman  and  Childs),  the  test 
of  "naming  60  words  in  three  minutes"  from  the  10th  year  (God- 
dard) to  the  15th  year  (Levistre  and  Morle",  Terman  and  Childs). 
The  assignment  of  such  a  test  to  a  single  age-level  becomes,  then, 
evidently  an  arbitrary  matter.  Over  against  these  are  other  tests 
that  show  great  constancy,  at  least  so  far.  Thus,  "counting  13 
pennies,"  "esthetic  comparison,"  "showing  right  hand  and  left 


alt  must  be  remembered  that  the  tables  and  materials  from 
which  Bell  had  to  construct  his  summary  have  been  assembled  so 
differently  by  the  different  investigators  that  their  gauging  of  the 
several  tests  is  not  really  directly  comparable,  so  that  Bell's  tables 
must  be  regarded  merely  as  a  preliminary  attempt  at  checking  up 
the  results  of  various  investigations. 


96     PSYCHOLOGICAL    METHODS   OF   TESTING   INTELLIGENCE 

ear"  fluctuate  in  rank-assignment  only  between  the  6th  and  the 
7th  years,  the  "recognition  of  omissions  in  drawings"  only  between 
the  7th  and  the  8th  years,  the  test  of  "counting  backward  from  20" 
only  between  the  8th  and  the  9th  year,  that  of  "naming  the  months" 
only  between  the  9th  and  the  10th  year.  The  "hard  problem-ques- 
tions" test  is  ranked  by  all  these  investigators  save  Goddard  in 
the  12th  year,  etc. 

It  will  be  seen  that  these  are  for  the  most  part 
tests  in  which  verbal  formulation  plays  little  or 
no  part.  It  is,  indeed,  quite  natural  that  where  the 
problem  and  its  answer  are  intimately  connected 
with  verbal  expression,  national  peculiarities  must 
make  themselves  evident;  but  it  will  be  possible  to 
reduce  this  source  of  error  if  more  heed  is  given  in 
the  future  to  the  transference  of  the  tests  from  the 
one  language  to  the  other  in  such  a  way  as  to  fit  as 
exactly  as  possible  the  linguistic  and  cultural  tone 
of  the  second  nation  and  thus  secure  equal  difficulty 
in  the  problems:  the  actual  verbal  translation  that 
has  been  used  by  many  investigators  has  often  failed 
to  meet  this  requirement.  Thus,  for  instance,  the 
rather  free  adaptation  of  the  method  that  Bobertag 
made  for  Germany  has  yielded  in  many  cases  re- 
sults in  closer  accord  with  those  of  Binet  than  have 
the  literal  translations  of  the  Americans. 

Finally,  we  shall  have  also  to  judge  the  value  of  a 
test  according  as  it  does  succeed  in  bringing  plainly 
to  light  differences  in  intelligence  that  are  known 
from  other  sources  to  exist.  On  this  point  Mile. 
Descoeudres  (46)  has  carried  out  a  study  of  the 
present  Binet  tests,  though,  to  be  sure,  upon  but  a 
limited  number  of  children.  She  tested  one  "intelli- 
gent" and  one  "unintelligent"  child  from  each  of  the 
six  years  of  a  boys'  and  of  a  girls'  Volksschule:  the 
selection  was  determined  by  the  teachers'  estimates 


THE  METHOD  OF  AGE  GRADATION 


97 


of  the  pupils'  intelligence.  "When,  now,  she  com- 
pared the  results  of  the  tests  for  the  12  unintelli- 
gent and  the  12  intelligent  children,  taken  as  groups, 
she  found  that  the  differentiation  of  the  two  groups 
appeared  with  quite  unequal  clearness  in  the  differ- 
ent tests.  Those  tests  in  which  the  intelligent  had 
the  clearest  advantage  over  the  unintelligent  (and 
that  therefore  have  the  most  claim  for  consideration 
as  tests  of  intelligence)  are  cited  in  the  first  column 
of  Table  XIV. 

TABLE   XIV 
BINET    TESTS    WHEREIN   A   CLEAB   DIFFERENCE   IS    SHOWN 


Between     Intelligent 
and     Unintelligent 
Normal       Children 
(Descoeudres). 

Between  Normal  and 
Feeble-Minded  Chil- 
dren (Chotzen). 

Between       Different 
Grades   of   Feeble- 
Minded       Children 
(Descoeudres). 

Arranging  5  weights. 
Definition  superior  to 
use. 
Counting  backward. 
Explanation    of    pic- 
ture. 
Noting    omissions    in 
drawings. 
Detecting  absurdities. 

Arranging  5  weights. 
Definition  superior  to 
use. 
Counting  backward. 
Comparison    of    two 
objects  from  mem- 
ory. 
Repeating  five  digits, 
16    syllables,     and 
the  story. 
Counting  coins. 
Making  change. 

Definitions. 
Description     of     pic- 
ture. 
Comparison    of    two 
objects  from  mem- 
ory. 
Problem-questions. 

Mile.  Descoeudres  has  also  undertaken  a  study  of 
feeble-minded  children  (73),  which  may  be  intro- 
duced here  for  comparison.  (We  shall  have  occa- 
sion to  discuss  it  in  more  detail  later  in  another  con- 
nection.) The  children  were  arranged  in  order  of 
the  estimated  degree  of  their  feeble-mindedness  and 
with  this  was  compared  their  capacity  in  15  differ- 
ent tests.  Among  these  tests  were  six  from  the 
Binet-Simon  series,  four  of  which  yielded  extraordi- 


98     PSYCHOLOGICAL   METHODS  OF  TESTING   INTELLIGENCE 

narily  high  correlations  (between  0.80  and  0.88) 
with  the  estimated  intelligence.  These  four  tests 
are  listed  in  the  third  column  of  Table  XIV.  With 
the  tests  of  "knowing  coins"  and  "naming  of  60 
words  in  three  minutes"  the  correspondence  was  of 
lesser  degree. 

And  thirdly,  we  must  call  to  mind  the  results  of 
Chotzen  to  which  we  have  already  referred  (p.  87), 
in  which  certain  tests  gave  far  clearer  expression 
than  others  to  the  difference  between  normal  and 
feeble-minded  children  of  the  same  age.  These  tests 
are  listed  in  the  second  column  of  the  table. 

It  is  worth  noting  that  most  of  the  tests  appear 
several  times  in  the  three  columns,  despite  the  fact 
that  the  three  investigations  were  carried  out  with 
children  of  quite  different  ages  and  under  otherwise 
varying  conditions.  This  shows  that  certain  tests 
are  particularly  fitted  to  bring  differences  in  intelli- 
gence out  in  clear  relief,  and  at  the  same  time  it 
shows  us  a  way  to  pick  out  these  true  tests  of  intelli- 
gence from  the  rest.24 

It  is  unnecessary  to  add  that  there  is  no  reason 
why  controls  like  these  should  be  limited  only  to  the 
tests  already  used  by  Binet;  in  fact,  comparisons 
between  intelligent  and  unintelligent  pupils  have  al- 
ready been  carried  out  for  the  most  varied  sorts  of 
tests  by  Meumann,  "Winteler,  Cohn-Dieffenbacher 
and  many  foreign  investigators.  From  these  and 
other  future  investigations  like  them  there  will  surely 

24There  is  one  other  point  of  correspondence  that  ought  to  be 
mentioned,  viz.,  that  the  differentiation  of  the  children  according 
to  their  social  status  was  also  revealed  for  the  greater  part  by 
these  same  characteristic  tests  as  revealed  the  intellectual  differ- 
entiation (see  pp.  53f.). 


THE  METHOD  OF  AGE  GRADATION  99 

be  found  certain  tests  of  so  decided  a  symptomatic 
value  that  they  will  deserve  to  be  adapted  for  intro- 
duction into  the  graded  system.  In  this  connection 
we  may  allude  among  others  to  the  modifications  of 
the  Masselon  test  recently  proposed  by  Meumann 
(v.  p.  16) — a  test  that  Meuinann  believes  is  usually 
solved  with  logical  insight  by  the  intelligent  but  not 
so  by  the  unintelligent. 

Investigations  in  correlational  psychology  of 
which  we  shall  speak  in  the  next  section  likewise 
afford  many  tests  whose  results  exhibit  decided  cor- 
respondence with  estimated  intelligence.  These 
tests  are  evidently  not  such  as  can  be  introduced 
directly  into  the  system  of  graded  tests  because  they 
deal  with  fine  gradation,  whereas  the  Binet  scale 
recognizes  only  tests  that  present  merely  the  al- 
ternatives "right"  or  "wrong."  Possibly,  how- 
ever, they  will  admit  of  rearrangement  into  a  sim- 
pler form  appropriate  to  the  scale. 

By  using  all  the  methodological  resources  that  we 
have  cited  we  shall  gradually  succeed  in  selecting 
tests  that  are  far  more  characteristic  of  the  intelli- 
gence of  a  given  age-level  than  those  now  in  use  and 
that  are  homogeneous  for  the  different  cultural 
groups  and  nations  to  be  tested. 

(b)  The  composition  of  series  for  the  several 
years.  Since  intelligence  is  a  formal  capacity  that 
can  be  determined  only  by  multiform  testing,  care 
must  be  taken  that  each  single  age-level  should  have 
a  manifold  of  tests.  It  is  not  enough,  therefore,  to 
put  together  any  sort  of  separate  tests  that  happen 
to  be  passed  by  75  per  cent,  of  those  of  the  age-level 
in  question.  If  the  tests  are  too  similar  to  one  an- 


100   PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

other,  their  combination  does  little  more  that  the 
testing  by  any  one  of  them  would  do.  Binet  and 
Simon  did  not  keep  this  principle  sufficiently  in 
mind :  some  of  their  age-levels  contain  only  linguistic 
tests  and  no  tests  of  activity. 

Furthermore,  the  age-levels,  considered  as  wholes, 
must  also  be  adjusted,  for  to  demand  that  particular 
tests  be  passed  and  to  demand  that  all  five  tests  of  a 
given  age-level  shall  be  passed  are  two  entirely  dif- 
ferent things.  This  adjustment  is  rendered  more  dif- 
ficult by  the  fact  that  in  computing  mental  age  one 
must  not  only  deal  with  the  tests  of  one  age-level,  but 
also  make  supplementary  use  of  tests  from  the  higher 
levels;  accordingly,  in  this  adjustment  of  the  levels 
as  a  whole  attention  must  be  paid  to  the  interrela- 
tion of  tests  that  come  into  consideration  in  connec 
tion  with  different  near-by  age-levels. 

The  controlling  principle  for  the  adjustment  or 
standardization  of  the  age-levels  is  that  approxi- 
mately symmetrical  distribution  of  the  mental  ages 
must  prevail  for  each  level.  That  is,  the  tests  are 
properly  arranged  and  skillfully  assembled  into  a 
system  if,  when  a  large  number  of  unselected  normal 
children  of  a  given  age  are  tested,  a  large  middle 
group  stand  'at  age'  and  the  rest  are  divided  fairly 
equally  between  advanced  and  retarded  cases. 

To  carry  out  such  investigations  practically  it 
will  be  necessary  to  try  as  many  tests  as  possible 
with  each  pupil ;  in  this  way  it  will  be  feasible  to 
assign  the  passing  of  each  particular  test  to  this  or 
that  age-level  and  to  discover  the  general  arrange- 
ment of  the  tests  that  furnishes  the  closest  to  a  sym- 
metrical distribution. 


THE  METHOD  OF  AGE  GRADATION  101 

The  investigation  can  be  made  with  more  pre- 
cision if  the  curve  of  distribution  be  based  upon  the 
mental  quotient  instead  of  the  mental  age,  for  we 
should  then  anticipate  fairly  good  correspondence 
between  the  curves  of  distribution  of  the  different 
age-levels.  The  mental  quotients  for  each  age-level 
would  then  be  grouped  together  in  10  per  cent, 
ranges,  i.  e.,  we  should  have  first  the  children  with 
mental  quotients  ranging  from  0.91  to  1.00  and  1.00 
to  1.10  that  would  form  the  compact  middle  group, 
then  on  either  side  of  them  groups  of  rapidly  dimin- 
ishing frequencies,  those  with  mental  quotients  .81 
to  .90,  .71  to  .80,  etc.,  below,  and  those  with  quotients 
1.11  to  1.20,  1.21  to  1.30,  etc.,  above. 

In  the  older  form  of  the  Binet-Simon  scale  the 
number  of  tests  assigned  to  each  year  differed.  In 
1911  Binet  put  five  tests  in  every  age;  it  is  to  be 
recommended  that  this  idea  of  uniformity  be  fol- 
lowed in  the  future  because  the  computation  of  the 
final  status  is  much  simplified  in  that  way.25 

(c)  The  extension  of  the  system.  In  the  next 
place  the  system  of  tests  is  to  be  extended  beyond 
its  present  limits  and  in  different  directions. 

Thus  far  the  lack  of  tests  has  been  most  seriously 
felt  in  the  upper  years.  The  tests  that  Binet  and 
others  have  devised  above  the  llth  year  have  been 
thus  far  quite  tentative  and  provisional ;  at  the  best 
they  could  furnish  us  the  necessary  supplementary 
material  for  the  ascertainment  of  mental  ages  10 
and  11,  but  they  absolutely  fail  to  provide  a  direct 

"Cf.  also  the  provisional  new  arrangement  of  Bobertag  in  Ap- 
pendix II. 


102   PSYCHOLOGICAL   METHODS  OP   TESTING   INTELLIGENCE 

measurement  for  the  mental  ages  12  to  15.  We  must 
admit  that  the  discovery  of  appropriate  tests  for 
these  higher  levels  of  mental  maturity  is  much  more 
difficult  than  for  the  younger  children,  but  the  diffi- 
culty is  to  be  overcome.  Thus,  Terman  and  Childs 
(64)  have  recently  proposed  a  series  of  tests,  each 
one  of  which  is  susceptible  to  diverse  gradings  with 
respect  to  the  capacities  that  it  requires,  so  that  it 
can  be  employed  up  to  mental  age  15.  Among  these 
tests  are  arithmetical  reasoning,  familiarity  with  a 
list  of  selected  words,  a  generalization  test  (discov- 
ering the  'moral'  of  a  fable  that  is  read  to  the  sub- 
ject) and  the  Ebbinghaus  completion  test  with  the 
task  made  progressively  more  difficult.26 

Let  us  hope  that  in  such  a  way  we  may  gradually 
advance  from  one  year  to  another  and  may  finally 
create  a  series  for  adults  as  the  termination  of  the 
whole  scale.  However,  this  problem  is  certainly  not 
so  easy  of  solution  as  Binet  thought  when  he  trans- 
ferred to  higher  ages  tests  that  he  had  originally  de- 
veloped for  the  years  11,  12  and  13,  and  made  the 
last  of  these  groups  over  into  tests  for  " adults"  by 
the  addition  of  two  new  ones. 

Another  thing  that  is  greatly  to  be  desired  is  an 
extension  of  the  system  by  the  creation  of  parallel 
series  of  tests  for  each  year.27  How  gladly  would 
we  use  the  method  to  trace  the  mental  development 
of  the  same  children  through  several  years;  but 
there  are  difficulties  in  the  way  of  this,  because,  of 
course,  when  the  same  tests  are  repeated,  the  child 

""See  Appendix  II. 
"Cf.  Binet,  36,  p.  163. 


THE  METHOD  OP  AGE  GRADATION  103 

confronts  them  with  a  different  attitude.28  But  if  we 
had  at  our  disposal  other  equivalent  series  of  tests,  it 
would  be  possible  to  make  repeated  testings  of  the 
same  individuals  more  frequently.  In  the  same  way, 
when  group  tests  were  carried  on,  those  children 
between  whom  there  might  be  danger  of  collusion 
could  be  tested  with  different  series.  Finally,  it  is 
valuable  to  have  a  supplementary  series  at  hand  in 
case  an  investigation  is  rendered  worthless  by  dis- 
turbance or  ineptitude  of  any  sort. 

When  we  shall  have  undertaken  simply  those  try- 
outs  of  a  considerable  number  of  single  tests  sug- 
gested above  (cf.  pp.  92  ff.),  we  shall  certainly  have 
enough  at  our  command  to  arrange  parallel  series 
for  each  year :  though  there  will  be  some  difficulty  in 
securing  an  approximate  equivalence  between  the 
corresponding  scales. 

There  has  been  some  demand  for  yet  another  kind 
of  extension  of  the  scale.  As  it  has  appeared  that 
the  mental  differences  are  extreme  between  one  year 
and  another  in  the  case  of  the  younger  children,  the 
need  has  been  felt  of  intermediate  stages,  as  for  in- 
stance for  specific  standards  for  such  age-levels  as 
6.5,  7.5  and  8.5  years.  In  our  opinion  this  need  is 
to  be  satisfied  in  another  way,  viz.,  by  use  of  the 
mental  quotient,  since  this  permits  us  to  take  frac- 

MBinet  had  five  9-year-old  children  tested  twice  with  the  same 
tests  with  a  14-day  interval.  On  the  average,  the  children  passed 
2.5  tests  more  on  the  second  trial — an  amount  that  would  signify 
an  increase  of  a  half-year  in  mental  age  (pp.  164-5).  As  Bobertag 
has  shown,  the  danger  resident  in  repetition  is  not  so  great  as  this 
when  the  interval  is  longer  (see  above,  p.  69)  ;  yet  even  under 
these  conditions  the  use  of  the  same  tests  is  but  a  make-shift  and 
a  second  and  a  third  repetition  of  the  same  tests  would  be  surely 
quite  out  of  the  question. 


104    PSYCHOLOGICAL   METHODS  OF   TESTING   INTELLIGENCE} 

tions  of  ages  into  account  without  special  half-year 
steps  (see  p.  105,  below). 

Finally,  mention  may  be  made  of  other  desires, 
curae  posterior es:  differentiation  of  the  scales  for 
children  of  different  social  strata,  for  the  two  sexes, 
and  especially  series  devoid  of  the  speech  factor  for 
the  testing  of  the  deaf  and  dumb,  etc. 

(d)  The  computation  of  the  final  values.  There 
are  two  main  difficulties  that  demand  our  attention 
here. 

The  one  consists  in  the  limitation  of  the  measures 
of  the  mental  age  and  the  chronological  age  to  whole ' 
numbers.  This  necessity  of  using  whole  numbers 
must  often  entail  an  arbitrariness  that  renders  im- 
possible the  carrying  out  of  the  method  with  pre- 
cision. 

For  instance,  a  child  who,  when  tested,  lacks  four  months  of 
completing  his  eighth  year  of  life,  must  of  necessity  be  classed  as 
"8  years."  If  he  passes  the  7-year-old  tests  and  two  more,  he  still 
receives  the  mental  age  of  7  years,  and  is,  accordingly,  credited 
with  a  mental  retardation  of  one  year,  although  in  reality  there  is 
practically  no  retardation  at  all. 

Bobertag29  tried  to  circumvent  this  difficulty  by 
taking  for  his  testing  only  those  children  that  were 
close  to  their  birthday  (at  least  within  2  months). 
But  usually  there  is  no  chance  for  free  choice  like 
this :  there  are  certain  children  to  be  tested,  regard- 
less of  what  their  age  happens  to  be  at  the  time.  Be- 
sides, that  kind  of  selection  at  most  only  lessens  the 
difficulty  for  the  chronological  age,  not  for  the  mental 
age.  The  failure  to  consider  the  two  or  three  ex- 
cess tests  passed  still  remains  as  a  defect  in  the  cal- 
culations. 

28  40,  I,  p.  110. 


THE    METHOD  OF  AGE  GRADATION  IDo 

Hence,  however  enticingly  simple  they  may  be,  we 
shall  have  to  give  up  the  use  of  the  rough  whole-year 
designations,  like  1,  2,  3  years  of  retardation,  and 
make  use  of  fractional  values:  it  is  enough,  of 
course,  to  carry  them  to  the  first  decimal  place.  In 
figuring  mental  age  each  single  test  passed  in  excess 
must,  then,  represent  a  fraction  of  a  year.  If,  for 
example,  two  of  the  five  8-year  tests  are  passed,  then 
2/5  is  to  be  added  to  the  mental  age;  the  child  in 
our  example  just  above  would  then  have  obtained  a 
mental  age  of  7.4  years.  Terman  and  Childs  (64) 
are  already  making  use  of  such  a  mode  of  calcula- 
tion, only  theirs  is  made  rather  awkward  by  the  pres- 
ence of  different  fractional  values  in  the  several 
years :  when  the  year  contains  seven  tests,  each  test 
has  only  the  value  one-seventh,  when  five  tests,  one- 
fifth.  This  feature,  too,  confirms  our  desideratum  al- 
ready expressed  that  every  one  of  the  years  should 
contain  just  five  tests,  then  each  test  would  have  the 
same  value,  0.2  of  its  year. 

But  now,  once  the  use  of  the  convenient  whole 
numbers  be  given  up,  every  objection  against  the  in- 
troduction of  the  mental  quotient  is  removed,  for  this 
furnishes  us  a  single  fractional  value  in  place  of  the 
two  fractional  values,  chronological  age  and  mental 
age.  This  quotient  lies  for  normal  children  in  the 
neighborhood  of  1.00  and  grades  off  continuously 
from  this  value  in  both  directions.  As  compared 
with  the  older  method  of  dividing  by  the  rough  units 
of  the  age-levels,  the  use  of  the  quotient  has  surely 
the  advantage  of  affording  a  certain  smoothness  and 
continuity  in  the  results,  since  the  fraction  (mental 
age  divided  by  chronological  age),  when  the  deci- 


106    PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

mals  are  used  in  each  term,  may  assume  any  value 
whatever.  Thus  the  mental  quotient  becomes  not 
only  a  useful  methodological  device  for  the  testing 
of  abnormal  children,  but  also  a  device  to  be  recom- 
mended for  use  with  normal  individuals.  We  have 
already  mentioned  (p.  101)  a  case  illustrative  of  its 
application. 

The  other  difficulty  of  calculation  pertains  to  the 
way  in  which  scattered  distribution  of  tests  passed 
is  handled  in  figuring  mental  age.  As  is  well  known, 
five  scattered  tests  must  be  passed  in  order  to  add 
one  year  to  the  mental  age,  but  no  attention  is  then 
paid  to  the  years  in  which  these  additional  tests  lie. 
Let  us  compare  the  two  hypothetical  examples  which 
follow : 

CHILD  A. 

All  tests  through  the  6th  year  are  passed :  hence  the  basis 

for  computation  is  a  mental  level  of 6  years 

also  passed  in  Age  7  two  tests  "I 
also  passed  in  Age  8  three  tests  I 
also  passed  in  Age  9  three  tests  J 
also  passed  in  Age  10  two  tests  J 

total  of  10  tests  =    2  years 


Resulting  mental  level 8  years 

CHILD  B. 

All  tests  through  the  6th  year  are  passed :  hence  the  basis 

for  computation  is  a  mental  level  of 6  years 

also  passed  in  Age    7  three  tests  " 
also  passed  in  Age    8  five  tests 
also  passed  in  Age    9  two  tests 
also  passed  in  Age  10  no  tests 

total  of  10  tests  =    2  years 

Resulting  mental  level 8  years 

There  seems  no  justification  for  equating  these 
two  children,  because  the  first  one  really  stands  de- 
cidedly higher  mentally  by  dint  of  his  conspicuously 


THE  METHOD  OF  AGE  GRADATION  107 

good  capacities  in  the  higher  levels.  To  be  correct, 
we  must  credit  more  difficult  tests  (those  lying  in 
higher  levels)  with  a  larger  fractional  value  than 
the  tests  normal  to  the  age  in  question  when  we  fig- 
ure in  these  higher  tests  for  addition  to  a  lower  age- 
level.  We  may  propose  a  method  of  calculation  for 
this  purpose,  that  is  not  too  complicated  and  that, 
like  the  mental  quotient,  takes  account  of  the  rela- 
tion of  the  several  years  to  each  other.  A  test  from 
a  higher  level  used  to  supplement  a  failure  in  a  lower 
level  shall  be  counted  not  merely  as  one  test,  but  as 
a  quotient  of  the  two  years  in  question. 

In  our  example  just  given,  then,  Child  A  would  be  figured  out 
thus :  basal  point,  mental  age  of  6  years ;  the  tests  from  the  four 
following  years  would  be  counted  in  this  way : 

Level  7  is  formed  by  2  tests  from  the  7th  year  (each  of  these 
counted  therefore  as  "1  test")  and  by  3  tests  from  the  8th  year, 
each  of  which  are  to  be  counted  as  8/7  test).  The  8th  year  would 
be  formed  by  3  tests  from  the  9th  year  (each  counting  9/8  test) 
and  2  tests  from  the  10th  year  (each  counting  10/8  test).  We  get, 
therefore,  as  total  additional  credits : 

2  x     1  =    2     tests 

8 

3  x  —  =    3.4  tests 

7 

9 

3  x  —  =    3-4  tests 
8 

10 

2  x  —  =    2.5  tests 
8 


11.3  tests 

Since  every  5  tests  are  worth  one  mental  year,  the  above  value 
indicates  a  supplement  of  11.3  4-  5  =  2.3  mental  years :  so  Child  A 
gets  a  mental  age  of  8.3  years. 

With  Child  B  it  works  out  thus :  the  2  tests  from  age  9  serve  to 


108   PSYCHOLOGICAL  METHODS  OF  TESTING  INTELLIGENCE 

supplement  age  7,  and  therefore  have  the  value  9/7  each,  the  re- 
maining 3  tests  in  the  7th  year  and  likewise  the  5  tests  in  the  8th 
year  count  for  their  own  level,  and  thus  figure  1  each. 

3  X    *     =    3     tests 

9 

2  x  —    =    2-6  tests 
7 

5  X    *     =5     tests 
10.6  tests 

These  10.6  tests  indicate  a  supplement  of  2.1  years ;  so  Child  B 
gets  a  mental  age  of  8.1  years  and  his  inferiority  to  Child  A  is 
now  brought  out  statistically. 


III.    Estimation  and  Testing  of  Finer  Gradations  of 
Intelligence 

(With  the  aid  of  the  method  of  ranks) 

1.     The  Problem 

The  different  degrees  of  intelligence  that  are  re- 
vealed by  the  Binet  method  are  relatively  gross: 
within  any  one  of  its  age-levels  there  are  possible 
other  and  very  much  finer  gradations  that  escape 
detection  by  its  tests.  Yet  these  very  differences  are 
often  enough  just  the  ones  of  consequence,  particu- 
larly whenever  we  are  dealing  with  the  members  or 
a  relatively  homogeneous  group.  If,  for  instance, 
we  are  comparing  the  pupils  of  a  school  grade  that 
are  of  approximately  the  same  age  and  of  corre- 
sponding school  training,  these  pupils  fall  mostly 
into  the  same  mental  level  according  to  the  Binet- 
Simon  tests,  yet  they  occupy  a  finely  graded  scale  of 
ranks  within  this  level.  Hence,  the  question  what 
place  a  pupil  occupies  among  those  of  his  age  or  of 
his  class  in  respect  to  intelligence  must  be  answered 
by  other  methods  that  seek  to  establish  a  rank-order 
of  the  individuals  concerned. 

Rank-orders  of  the  pupils  of  a  class  can  be  estab- 
lished in  quite  different  ways.  In  the  first  place 
there  is  the  school  or  pedagogical  rank-order  that  is 
based  on  school  performances.  Thus  we  number  the 
pupils  according  to  the  outcome  of  a  school  exercise : 

109 


110    PSYCHOLOGICAL   METHODS   OF   TESTING    INTELLIGENCE 

the  departmental  teacher  ranks  them  at  the  end  of 
the  term  on  the  totality  of  their  work  in  his  subject : 
finally,  all  these  ranks  in  different  subjects  are  com- 
bined into  a  rank-order  for  the  school  certificate  in 
which  every  pupil  is  assigned  his  "class-place." 

Since  these  rank-orders  are  always  available,  it  is 
but  natural  to  employ  them  for  our  problem,  and 
this  is  what  actually  happened  very  often  in  the 
early  stages  of  the  experimental  study  of  intelli- 
gence. Thus,  for  example,  Ebbinghaus  (5)  divided 
his  subjects  into  three  sections  on  the  basis  of  their 
class-marks  in  order  to  determine  whether  the  dif- 
ferent groups  responded  with  different  degrees  of 
success  to  his  completion  tests.  Other  investigators 
had  the  teachers  select  a  number  of  'good'  and  'poor' 
scholars  in  order  to  make  comparison  of  their  be- 
havior under  experimentation. 

Yet,  however  convenient  this  ever-ready  classifica- 
tion may  be,  it  is  not  at  all  adequate  for  our  pur- 
poses, because  the  implicit  assumption  that  under- 
lies such  uses  of  the  class-marks — that  school  per- 
formance is  an  absolutely  accurate  indication  of  in- 
telligence— is  unjustified.  The  results  obtained  by 
the  Binet-Simon  method  have  already  shown  this 
(see  p.  59),  and  other  statistical  data  will  confirm  it. 
As  a  matter  of  fact,  every  school  man  who  is  blessed 
with  psychological  insight,  knows  it  himself. 

We  need,  then,  a  rank-order  that  is  based  directly 
upon  the  degree  of  intelligence  of  the  pupils. 

Such  an  order  does  not  exist  in  the  ordinary  school 
system,  and  must  therefore  first  be  created  ad  hoc. 
There  are  available,  again,  two  different  ways  of  ac- 
complishing this  aim :  either  the  teacher,  on  the  basis 


ESTIMATION    AND   TESTING   OF   FINER   GRADATIONS       111 

of  everything  that  he  knows  about  his  pupils,  may 
estimate  their  intelligence  and  arrange  them  ac- 
cording to  his  estimate  (see  the  next  section)  or  we 
can  apply  experimental  tests  of  intelligence,  the  out- 
come of  which  admits  of  arranging  the  pupils  in  a 
series.  Bank-orders  of  intelligence  are  therefore 
divided  into  orders  based  on  estimates  and  orders 
based  on  tests. 

In  the  last  resort  the  second  of  these  divisions 
brings  us  to  the  question :  Is  it  possible,  on  the  basis 
of  a  short  examination  with  a  series  of  tests  to  arrive 
at  a  gradation  of  pupils  that  corresponds  with  their 
actual  differences  of  intelligence  and  such  that  the 
rank  that  each  gains  is  sufficiently  characteristic  vf 
his  grade  of  intelligence  within  the  group? 

It  is  not  hard  to  obtain  a  rank-order  on  the  basis 
of  a  test  or  of  a  series  of  tests.  To  be  sure,  the  Binet 
tests,  most  of  which  admit  of  a  choice  between  the 
evaluations  'right'  or  'wrong,'  are  not  fitted  for  that 
purpose,  but  we  can  obtain  a  gradation  in  all  those 
tests  that  bring  into  operation  a  measurable  per- 
formance, in  which  what  is  measured  is  the  quantity 
of  the  performance  in  a  given  time  or  the  quality  of 
the  performance  (as  indicated  by  the  number  of  er- 
rors). Every  test  of  this  sort  creates  an  array  of 
ranks,  only  it  remains  to  discover  how  much  the  ob- 
tained order  may  inform  us  about  the  intelligence  of 
the  examinees. 

Hence  we  need  here,  too,  a  device  for  guaging  our 
work,  and  this  device  consists  in  the  comparison  of 
several  rank-orders  obtained  with  the  same  individ- 
uals by  means  of  the  method  of  correlation. 

The  method  of  calculating  correlation  can  not,  of 


112   PSYCHOLOGICAL   METHODS   OF  TESTING   INTELLIGENCE 

course,  be  developed  here.1  We  merely  point  out 
here  that  a  correlation  =  1.00  means  that  there  is 
complete  correspondence  between  the  two  rank-or- 
ders (or  groups).  A  correlation  —  0  means  com- 
plete absence  of  correspondence.  The  size  of  the 
decimal  fraction  between  0  and  1,  then,  shows  the 
degree  of  correspondence.  The  probable  error 
(P.  E.)  is  a  measure  of  reliability:  only  when  the 
correlation  amounts  to  at  least  three  times  the  size 
of  its  probable  error  is  a  real  significance  to  be 
ascribed  to  it.  In  details  the  methods  used  by  differ- 
ent investigators  for  calculating  the  coefficient  of  cor- 
relation show  considerable  differences.  The  appen- 
dix contains  an  example  of  the  simplest  method  of 
calculating  rank-correlation  as  I  have  used  it. 

All  the  different  rank-orders  that  have  been  named 
can  be  brought  into  correlation  with  one  another :  of 
these  possible  correlations  we  shall  have  to  deal  for 
our  purposes  with :  correlation  of  test  with  test,  cor- 
relatign  of  estimates  with  school  performance,  cor- 
relation of  tests  with  estimates. 

Correlations  of  tests  with  tests  have  been  worked 
out  in  particular  by  Spearman  (77,  79,  80).  If  the 
pupils  of  a  class  have  been  tested  by  means  of  sev- 
eral different  tests  and  the  resulting  rank-orders 
show  mutual  high  correlation,  this  is,  in  Spearman's 
opinion,  a  sign  that  the  capacity  operative  in  the 
tests  depends  upon  a  common  factor  (Spearman 
uses  the  expression  " general  intelligence"  or  "gen- 
eral ability").  This  brings  it  about  that  Pupil  A 

*A  general  exposition  of  these  methods  will  be  found  in  Betz 
(70)  and  Stern  (1,  chs.  19  and  20).  [Also  in  the  translator's 
Manual  of  Mental  and  Physical  Tests,  Ch.  3.] 


ESTIMATION  AND   TESTING  OP  FINER  GRADATIONS       113 

ranks  high  in  the  discrimination  of  line-lengths,  in 
memory  for  nonsense  syllables,  etc.,  while  Pupil  Z 
ranks  low  in  each  of  these  functions.  For,  if  the  re- 
sult were  conditioned  by  specific  abilities,  a  given 
pupil  would  occupy  very  different  ranks  in  the  dif- 
ferent tests.  Spearman  has,  indeed,  found  ex- 
traordinarily high  correlations  in  some  instances: 
on  this  account  he  holds  it  to  be  demonstrated  that 
there  really  is  such  a  thing  as  general  intelligence, 
and  that  its  grade  can  be  experimentally  determined 
by  tests  that  correlate  to  a  high  degree  with  one  an- 
other. 

We  can  agree  with  the  first  of  these  conclusions. 
We  have  already  alluded  frequently  in  what  has 
gone  before  to  the  'general'  and  ' formal'  character 
of  intelligence,  whose  influence  is  operative  in  activi- 
ties of  widely  differing  character.  Of  course,  we 
must  admit  that  this  influence  of  intelligence  is 
never  more  than  approximately  uniform,  that  within 
the  " general  intelligence"  of  every  person  there 
exist  certain  specially  strong  and  certain  specially 
weak  points,  so  that  a  truer  picture  of  the  total  in- 
telligence of  the  individual  is  given  by  the  idea  of  a 
mutual  balancing  or  compensation  of  different  capac- 
ities than  by  the  idea  of  their  equality  or  corre- 
spondence. 

But  just  here  does  the  value  of  Spearman's 
method  for  the  testing  of  intelligence  become  dubi- 
ous. If  we  select  four  or  five  tests  that  show  very 
high  intercorrelations  in  order  to  use  their  totals  as 
a  measure  of  intelligence,  there  exists  the  danger 
that  we  may  be  testing  by  them  only  a  very  restricted 
portion  of  the  field  of  intelligence  and  leaving  en- 


114   PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

tirely  out  of  consideration  other  compensatorily  im- 
portant portions.  If,  on  the  other  hand,  we  keep  the 
idea  of  compensation  in  mind  and  therefore  assemble 
together  tests  that  correlate  only  moderately  with 
one  another,  we  have  no  way  of  knowing  which  com- 
bination of  tests  does  actually  secure  that  mutual 
balance  on  the  basis  of  which  as  a  whole  a  more  cor- 
rect quantitative  expression  of  intelligence  is  to  be 
yielded. 

To  the  first  of  these  points  it  can  of  course  be  re- 
plied: we  can  select  tests  that  show  a  high  correla- 
tion from  such  divergent  realms  of  mental  life  that 
we  shall  avoid  the  danger  of  testing  only  a  very  re- 
stricted portion  of  the  field  of  intelligence.  But,  in 
opposition  to  this,  attention  must  be  directed  to  a 
matter  that  has  not  been  sufficiently  heeded  hereto- 
fore. All  test  investigations,  even  if  they  pertain  to 
the  most  widely  different  realms  of  mental  life,  have 
this  in  common  that  they  are  experimental  modes  of 
procedure,  so  that  all  put  the  examinee  into  the  same 
mental  condition — that  of  being  a  subject.  And  this 
involves  not  only  very  definite  adjustments  of  atten- 
tion, of  mood,  etc.,  but  also  in  particular  the  habit  of 
mere  reacting,  of  taking  at  a  given  moment  a  re- 
ceptive attitude  toward  a  problem  set  from  without. 
Consequently,  spontaneous  intelligence  is  excluded 
by  the  conditions  of  the  experiment ;  there  is  not  in- 
volved that  intelligence  that  sets  its  own  problems, 
that  thinks  out  things  independently  beyond  what  is 
immediately  given,  that  anticipates  explanations  by 
questions,  and  that  in  the  real  situations  of  life 
quickly  works  out  the  best  way  of  confronting  a  sit- 
uation. And  we  have  absolutely  no  way  of  knowing 


ESTIMATION   AND   TESTING  OF  FINER  GRADATIONS       115 

whether  we  can  infer  from  the  reactive  intelligence, 
however  many  tests  of  it  we  make,  to  this  spontane- 
ous intelligence.  It  is  possible  that  certain  tests  or 
certain  combinations  of  tests  have  a  fairly  high  cor- 
relation with  the  spontaneous  intelligence,  but  that 
is  something  that  can  not  be  determined  from  the  ex- 
periments. 

Hence  the  mere  comparison  of  tests  with  one  an- 
other affords  us  neither  a  clear  insight  into  the  neces- 
sary compensations,  nor  a  decision  as  to  the  sympto- 
matic value  of  the  testing;  rather  must  we  seek  the- 
means  of  guaging  the  tests  in  some  criterion  that  lies 
outside  of  experiment.  Such  a  criterion  is  supplied 
by  the  estimation  of  the  pupils  made  by  the  teacher. 

It  follows  that  this  estimation  of  intelligence  by 
the  teacher  thus  comes  to  possess  a  methodological 
significance  of  its  own,  for  it  can  be  set  up  as  a  stand- 
ard for  the  comparison  of  other  rank-orders,  i.  e., 
those  obtained  experimentally,  only  when  we  have 
first  made  sure  of  its  own  nature  and  its  reliability. 
There  are  two  ways  of  going  about  this ;  the  one  is 
by  analysis  of  the  procedure  of  the  teacher  when  he 
does  the  estimating  of  his  pupils'  intelligence,  the 
other  is  by  determining  objectively  to  what  extent 
his  estimation  is  dependent  upon  what  he  knows 
about  the  pedagogical  rank-order  of  the  children, 
their  places  in  the  class  or  their  examination  marks, 
etc. 

So,  only  when  we  have  first  discovered  whether 
the  estimated  intelligence  is  a  useful  means  of  con- 
trol or  under  what  precautions  it  is  useful,  can  the 
real  experimental  problem  be  attacked: — the  prob- 
lem of  finding  out  those  combinations  of  tests  that 


116    PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

correlate  to  a  high  degree  and  with  great  uniformity 
with  a  reliable  set  of  estimations  of  intelligence. 
This  matter  will  be  the  subject  of  the  three  sections 
that  follow. 

2.    The  Teacher's  Estimation  of  the  Intelligence  of 
his  Pupils 

The  question  whether  a  teacher  is  really  able  to 
estimate  the  degree  of  intelligence  of  his  pupils  is 
one  that  has  no  little  importance  even  outside  of  our 
special  and  limited  problem.  It  is  surely  practically 
worth  while  for  the  teacher,  who  is  accustomed  ordi- 
narily to  pass  judgments  about  his  pupils  primarily 
on  the  basis  of  their  objective  performance,  to  try 
for  once  to  decide  whether  and  to  what  extent  a  cer- 
tain capacity,  namely  general  intelligence,  is  con- 
cerned in  these  performances.  He  will  be  obliged  to 
study  his  pupils  more  carefully,  to  analyze  their  in- 
dividual disposition,  and  will  perhaps  come  by  this 
means  to  a  better  valuation  of  their  work,  to  conclu- 
sions as  to  choice  of  curriculum,  to  advice  as  to  the 
choice  of  vocations. 

The  estimation  of  intelligence  has  an  advantage 
over  the  experimental  testing  of  intelligence  in  the 
fact  that  it  is  based  upon  longer  and  wider  acquaint- 
ance with  the  pupil.  For  months  the  teacher  has 
watched  the  behavior  of  a  pupil  in  the  oral  and  writ- 
ten tasks  of  different  studies,  has  noted  his  ques- 
tions and  answers,  his  interest  or  his  indifference 
when  dealing  with  many  different  subjects,  his  inde- 
pendence or  his  need  of  assistance  in  his  work,  and 
has  seen  as  well  his  behavior  when  among  his  mates, 
in  play  in  the  school  yard,  on  excursions,  etc.  He 


ESTIMATION  AND  TESTING  OP  FINER  GRADATIONS       117 

has,  then,  a  much  broader  range  of  information  on 
which  to  base  his  judgment  of  the  pupil's  intelli- 
gence than  has  the  experimenter,  who  has  merely 
taken  a  half -hour's  time  to  record  the  response  of 
the  child  to  a  small  number  of  tests.  But,  on  the 
other  hand,  there  are  some  great  disadvantages  in 
this  method.  The  teacher  does  not,  as  a  rule,  stop 
to  consider  on  what  concrete  facts  of  observation 
his  judgment  is  based:  the  symptoms  which  de- 
termine his  judgment  are  not  controllable  as  regards 
their  real  importance;  when  the  intelligence  of  sev- 
eral pupils  is  compared,  the  comparison  is  based  on 
different  facts  that  are  not  strictly  comparable  with 
one  another.  Finally,  the  teacher  is  often  by  no 
means  clear  as  to  what  he  is  to  understand  by  '  intel- 
ligence' when  he  makes  his  decisions. 

These  considerations  are  enough  to  show  that  the 
estimation  of  intelligence  is  far  from  an  easy  matter, 
that  it  is  not  something  to  be  demanded  of  every 
teacher  as  a  matter  of  course.  What  is  desired  here 
is  to  seek  the  middle  road  between  two  opposite 
sources  of  danger:  on  the  one  hand  we  are  threat- 
ened with  the  danger  that  the  teacher  can  not  free 
himself,  when  he  estimates  intelligence,  from  the 
pedagogical  habit  of  judging  his  pupils  by  their 
schoolroom  performance,  in  which  event  the  rank- 
order  for  intelligence  will  be  no  more  than  a  copy  of 
the  rank-order  for  class  work,  corrected  in  a  few 
points.  If  the  teacher  tries  to  avoid  this  tendency, 
then  there  arises  the  other  danger  that  he  goes  at 
the  selection  blindly  and  that  the  resulting  rank- 
order  becomes  a  mere  product  of  chance. 

Evidently,  the  estimating  of  intelligence  by  the 
teacher  makes  contribution  not  only  to  the  psychol- 


118   PSYCHOLOGICAL   METHODS  OF   TESTING   INTELLIGENCE 

ogy  of  the  pupils,  but  also  to  the  psychology  of  the 
teacher.  Teachers  will  vary  a  great  deal  in  their 
capacity  to  undertake  this  work  of  estimating  intelli- 
gence, so  that  for  scientific  investigations  it  becomes 
methodologically  essential  that  tests  shall  not  be  com- 
pared with  any  sort  of  estimation  of  intelligence 
made  by  any  sort  of  teacher,  but  that  for  this  purpose 
teachers  specially  trained  and  specially  gifted  in 
psychology  must  be  sought  out  and  instructed  spe- 
cifically in  the  nature  of  the  task  demanded  of  them. 
An  entertaining  as  well  as  instructive  inquiry  on 
this  subject  has  been  made  by  Binet  (36;  71). 

He  sent  to  numerous  elementary  school  teachers  a  questionary 
asking  them  to  state:  1st,  to  what  extent  they  thought  that  error 
might  creep  in  when  teachers  sought  to  judge  the  intelligence  of 
their  pupils,  and  2d,  what  method  they  would  pursue  in  order  to 
arrive  at  an  accurate  estimate  of  intelligence.  Binet  soon  saw 
that  he  had  thus  found  an  excellent  scheme  for  classifying  the 
intelligence  of  the  teachers. 

The  first  question  was  not  very  well  put.  The  answers  simply 
showed  that  there  were  some  optimists  who  thought  that  they 
practically  never  made  any  mistake  in  appraising  the  intelligence 
of  their  pupils,  while  others  were  ready  to  admit  that  they  might 
be  mistaken  in  one  case  in  every  three.  Not  much  else  came  out 
of  this  question. 

The  answers  to  the  second  question  were  much  more  fruitful. 
The  greatest  variety  of  ideas  concerning  the  nature  of  intelligence 
was  exhibited:  all  possible  attempts  at  defining  it  were  made — all 
the  way  from  the  scholastic  narrow-mindedness,  which  conceives 
intelligence  as  nothing  but  the  capacity  to  acquire  information,  up 
to  the  neat  formulation  of  one  woman : 

"L'intelligence  ne  sert  pas  settlement  3.  apprendre,  elle  sert 
surtout  a  'faire  sa  vie.' "  And  the  symptoms  on  which  the  teach- 
ers base  their  judgment  of  intelligence!  It  is  declared  that  heed 
must  be  given  to  heredity,  since  higher  intelligence  is  to  be  ex- 
pected from  children  of  more  intelligent  parents.  It  is  recom- 
mended to  take  note  of  the  facial  expression ;  the  more  intelligent 
child  is  easily  distinguished  from  the  mentally  lazy,  dull  child  by 
his  vivacious,  open,  mobile  countenance.  Some  of  the  teachers  lay 
stress  on  observation  of  their  pupils  during  periods  of  free  play, 
and  would  regard  as  intelligent  children  that  displayed  initiative 
and  creative  tendencies  there.  But  the  chief  insistence  is  laid,  as 


ESTIMATION  AND   TESTING  OP  FINER  GRADATIONS        119 

would  be  expected,  upon  the  behavior  of  the  child  under  instruc- 
tion, and  the  attempt  is  made,  with  more  or  less  success,  to  dif- 
ferentiate the  strictly  intellectual  factors  in  the  school  work  from 
the  phases  that  depend  more  on  mere  memory:  quickness  of  ap- 
prehension, ability  to  solve  problems  in  applied  mathematics,  un- 
derstanding of  historical  movements  and  relations,  good  orthog- 
raphy, expressive  reading  and  many  other  things  are  mentioned 
as  symptoms  that  serve  the  teachers  for  estimating  theii^  pupils' 
intelligence.  Finally,  even  the  teachers  themselves  hit  on"he  use 
of  the  method  of  tests  by  asking  of  their  pupils  certain  questions, 
specially  prepared  for  the  purpose,  the  answers  to  which  serve 
them  as  a  measure  for  guaging  intelligence. 

Biiiet  then  enters  into  a  very  careful  criticism  of 
these  various  ideas,  calls  attention  to  the  strong  and 
the  weak  features  in  them,  shows  that  the  "  intelli- 
gence questions"  invented  for  the  express  purpose 
are  much  less  useful  than  the  tests  worked  out  by 
the  psychologist  after  long  years  of  experimentation, 
and  comes  to  the  conclusion  that  the  estimation  of 
intelligence  by  the  teacher  is  not  at  all  likely  to 
render  the  exact  testing  of  intelligence  a  superfluous 
process.  It  must  be  admitted  that  he  might  easily 
have  given  more  emphasis  to  the  reverse  of  this 
statement:  he  might  have  pointed  out  that  the  esti- 
mation of  intelligence  may  possess  advantages  that 
are  excluded  on  principle  from  the  mere  test,  so  that 
the  estimation  may  therefore  be  indispensable  as  a 
supplement,  and  also  in  part  as  a  control  for  the  re- 
sults of  tests.2 


This  whole  discussion  of  Binet's  is  couched  in  a  light  and 
sketchy  vein,  but  is  on  that  account  one  of  the  prettiest  examples 
of  the  grace  of  his  style  and  the  pictorial  clarity  of  his  phrases. 
We  may  cite  here  just  two  instances  that  are  so  neatly  put  as  to 
defy  translation.  Where  he  is  speaking  of  the  ease  with  which  the 
possession  of  information  may  be  misinterpreted  as  token  of  in- 
telligence, he  says :  "La  rnSrnoire  est  la  grande  simulatrice  de 
1'intelligence."  And  the  recommendation  to  watch  children  while 
engaged  in  play  as  well  as  in  school  is  coupled  with  the  declara- 
tion :  "En  classe  ils  sont  d6natur6s  par  la  discipline." 


120    PSYCHOLOGICAL   METHODS   OF  TESTING   INTELLIGENCE 

We  shall  bring  together  next  the  chief  require- 
ments that  a  teacher  must  keep  in  mind  when  he  un- 
dertakes an  estimation  of  intelligence  if  it  is  to  be 
usable  for  scientific  purposes. 

He  should  conceive  of  intelligence,  just  as  we  de- 
fined it  at  the  beginning  of  this  monograph,  as  ' '  gen- 
eral mental  adaptability  to  new  problems  and  condi- 
tions of  life, ' '  should  give  particular  heed  to  the  two 
attributes  " general"  and  ''adaptation  to  the  new," 
and  should  guard  against  identifying  with  intelli- 
gence any  sort  of  special  ability  or  the  mere  posses- 
sion of  information  or  readiness  in  speech.  Because 
of  the  general  nature  of  intelligence  it  is  essential  to 
take  into  consideration  the  way  in  which  the  child 
behaves  in  quite  different  situations  and  when  con- 
fronted by  problems  of  varied  sorts. 

But,  now,  it  is  of  the  essence  of  the  estimation  of  in- 
telligence that  not  only  shall  each  pupil  be  judged  in- 
dividually, but  he  shall  also  be  compared  with  the 
other  pupils  and  be  placed  in  a  definite  relation  of 
equality  or  inequality  with  them.  For  this  purpose 
of  comparison  there  is  to  be  laid  down  a  rule  that,  de- 
spite its  fundamental  character,  has  by  no  means  al- 
ways been  observed :  Only  those  pupils  shold  be  lo- 
cated in  a  given  rank-order  of  intelligence  that  are 
sufficiently  like  one  another  in  other  respects.  The 
reason  is  that  the  slight  differences  of  intelligence  that 
have  to  be  considered  in  making  the  estimation  have 
significance  only  when  on  the  common  basis  of  an 
otherwise  homogeneous  group.  For  this  reason  the 
comparative  estimation  of  intelligence  has  usually 
been  restricted  to  the  pupils  of  a  single  class ;  but  it  is 
necessary  as  well  to  be  careful  to  secure  homo- 


ESTIMATION  AND   TESTING  OF  FINER  GRADATIONS       121 

geneity  within  the  class,  not  only  by  excluding  chil- 
dren who  are  plainly  abnormal,  but  also  by  limiting 
the  estimation  to  a  definite  range  of  ages.  If,  for  in- 
stance, in  the  5th  school  year,  normally  corresponding 
to  ages  10-11  years,  the  class  contains  some  13-year- 
old  boys,  they  should  not  be  included  in  a  rank-order 
of  intelligence,  for  the  teacher  is  not  in  a  position  to 
determine  what  portion  of  the  intelligence  that  they 
exhibit  is  to  be  ascribed  to  their  greater  age:  that 
would  have  to  be  deducted  even  if  they  were  com- 
pared to  11-year-old  children.  Hence,  you  must  first 
sort  out  any  class  within  which  you  would  undertake 
an  estimation  of  intelligence.  It  is  impossible  to  lay 
down  any  hard  and  fast  rule  for  this :  the  range  of 
ages  that  should  be  included  depends  on  different 
circumstances ;  a  greater  latitude  of  age  is  permissi- 
ble in  maturer  than  in  the  younger  years.  In  gen- 
eral, the  calculations  that  I  shall  speak  of  below  in- 
dicate that  some  20  to  25  per  cent,  of  the  members  of 
every  class  must  be  excluded. 

The  arrangement  of  the  pupils  on  the  basis  of  their 
intelligence  can  be  by  groups  or  in  a  serial  order.  The 
first  of  these  arrangements  is  far  easier  for  the 
teacher.  In  fact,  he  is  accustomed  to  classify  almost 
all  things  that  are  judged  in  terms  such  that  four  to 
six  classes  are  formed ;  and  a  similar  schema  can  be 
applied  to  intelligence — as,  for  example,  in  the  form : 
I  very  high  intelligence,  II  good,  III  medium,  IV 
slight,  V  very  weak  intelligence.  Thus,  Pearson  and 
those  of  his  followers  who  have  made  use  of  estima- 
tions of  intelligence  in  their  statistical  investigations 
of  school  children  have  been  content  with  groupings 
of  this  sort  (74,  76,81). 


122   PSYCHOLOGICAL    METHODS   OF   TESTING    INTELLIGENCE 

Personally,  I  do  not  find  much  to  recommend  in 
the  method.  Even  though  most  of  the  pupils  can  be 
located  without  difficulty  in  one  of  the  five  groups, 
there  still  remains  a  fairly  large  number  of  pupils 
with  whom  the  teacher  remains  in  doubt  as  to  which 
of  two  adjacent  groups  they  may  belong  to.  The 
final  decision  is  then  an  arbitrary  one,  which,  if  often 
enough  repeated,  can  destroy  the  value  of  the  whole 
distribution.  If,  for  instance,  three  such  doubtful 
cases  are  assigned  to  Group  II  the  proportioning  of 
cases  and  the  resulting  correlations  are  quite  differ- 
ent from  what  they  would  be  if  these  cases  had  been 
assigned  to  Group  III,  where  they  might  just  as 
properly  be  placed.  It  follows  that  so  small  a  num- 
ber of  groups  as  this  is  entirely  inadequate  for  the 
most  important  problems  of  correlation.  Many  of 
our  tests  yield  finely  graded  rank-orders  of  pupils, 
and  so  it  is  to  be  desired  that  the  estimated  intelli- 
i  gence  with  which  these  tests  are  to  be  related  should 
also  take  the  form  of  a  rank-order. 

The  construction  of  a  rank-order  of  all  pupils 
based  on  estimations  of  their  intelligence  in  this  way 
naturally  presents  many  difficulties.  Many  persons 
hold  it  as  a  matter  of  course  to  be  quite  impossible. 
But  experience  has  shown  that  the  task  can  be  done. 
The  division  into  groups  that  we  have  just  dis- 
cussed can,  indeed,  be  carried  out  as  a  preliminary 
step ;  then  the  pupils  within  each  of  the  groups  must 
be  further  arranged  in  a  scale,  so  far  as  practicable. 
At  the  limits  of  the  groups,  however,  care  must  be 
taken,  for  it  has  been  shown  many  times  that  shifts 
will  have  to  be  made  at  these  points,  as,  for  instance, 
a  child  originally  assigned  to  Group  II  has  to  be 


ESTIMATION  AND  TESTING  OF  FINER  GRADATIONS       123 

placed  after  the  children  lying  in  the  upper  section 
of  Group  III. 

But,  on  the  other  hand,  the  principle  of  rank-ar- 
rangeinent  must  not  be  carried  so  far  as  to  insist  on 
assigning  a  precise  place  to  every  child  at  any  cost. 
Often  enough,  especially  in  the  middle  region,  it  will 
be  felt  to  be  an  arbitrary  matter  to  give  N  a  poorer 
place  than  M,  because  it  will  have  been  impossible 
to  arrive  at  an  unequivocal  judgment  as  to  the  differ- 
ence in  the  worth  of  the  intelligence  displayed  by  the 
two  children.  The  rule  for  such  cases  is  to  give  the 
same  rank-number  to  individuals  of  equivalent  abil- 
ity, using  the  number  that  corresponds  to  the  aver- 
age of  the  places  that  they  occupy.  Thus,  if  four 
individuals  that  would  have  occupied  the  stations 
5,  6,  7  and  8  seem  of  equal  intelligence,  each  one  re- 

5+6+7+8 

ceives  the  rank-number  6.5,  i.  e.,   =6.5. 

4 

In  case  this  process  has  to  be  followed  repeatedly, 
the  number  of  rank-differences  that  are  at  our  dis- 
posal is  reduced,  but  this  disadvantage  is  more  than 
compensated  for  by  the  advantage  of  avoiding  arbi- 
trariness in  the  arrangement.  It  is  no  misfortune 
if  no  more  than  20  or  even  a  dozen  different  rank- 
numbers  are  forthcoming  in  the  ranking  of  a  class  of 
30  pupils. 

We  shall  be  obliged  to  dwell  somewhat  longer  on 
the  matter,  already  broached,  of  the  dependence  of 
the  series  of  estimations  on  the  pedagogical  rank- 
order.  The  greater  the  role  played  by  the  school's 
rank-order  in  the  ordinary  management  of  the  class, 
the  greater  will  be  this  dependence.  But  there  pre- 


124   PSYCHOLOGICAL    METHODS   OF  TESTING   INTELLIGENCE 

vail  decided  differences  with  regard  to  the  class- 
marks.  The  plan,  which  was  formerly  quite  gener- 
ally followed,  whereby  each  pupil  had  a  "class- 
place,"  which  determined  his  rank  among  his  class- 
mates for  a  quarter  of  a  year,  is  now  becoming  less 
and  less  common.  Sometimes  the  statement  of 
standing  is  accompanied  by  a  designation  of  place  in 
the  class,  e.  g.,  "promoted  as  15th  in  a  class  of  27," 
without  laying  any  further  special  stress  on  the 
ranking ;  sometimes  even  this  designation  is  lacking, 
so  that  there  exists  no  positive  school  rank-order  at 
all.  Of  course,  even  where  there  is  a  school  rank- 
order,  it  is  to  be  desired  that  the  teacher  work  out 
his  estimation  of  intelligence  as  far  as  possible  inde- 
pendently of  this  school  ranking.  On  this  account 
it  is  in  every  way  objectionable  to  proceed,  as  is  often 
done  because  it  is  the  easiest  way,  by  taking  the 
school  ranking  as  a  starting  point  and  simply  shift- 
ing the  position  of  those  children  whose  rank  in  this 
list  has  been  displaced  by  some  special  circumstance, 
like  illness,  transfer  of  school,  evident  laziness,  etc. 
Burt,  for  example,  worked  in  that  way.  To  be  sure, 
such  a  "corrected  school  ranking"  is  doubtless  bet- 
ter than  an  uncorrected  one  for  psychological  pur- 
poses, but  it  by  no  means  presents  a  correct  ranking 
of  intelligence. 

To  secure  as  impartial  a  ranking  of  intelligence  as 
possible,  the  following  procedure  may  be  recom- 
mended. Write  the  names  of  each  of  the  pupils  to 
be  ranked  on  a  separate  card,  and  arrange  these  first 
in  alphaljetical  order.  Then  and  only  then  sort  out 
the  cards  into  different  groups  for  their  intelligence, 
and  finally  try  to  settle  upon  rankings  within  each 


ESTIMATION  AND  TESTING  OP  FINER  GRADATIONS       125 

group.    The  series  thus  secured  is  then  noted  down 
with  the  proper  number  for  each  individual. 

It  is  an  excellent  plan  to  do  the  work  all  over  again 
after  an  interval  of  perhaps  three  or  four  weeks,  and 
without  referring  to  the  series  first  obtained.  The\ 
degree  of  correspondence  between  the  two  estima- 
tions is  then  to  be  determined  by  the  correlation 
method.  Only  if  the  coefficient  of  reliability  is  high, 
i.  e.,  if  the  two  series  are  very  similar  to  one  another, 
should  they  be  made  the  basis  of  further  investiga- 
tions. If  they  are  then  to  be  used,  it  is  best  to  con- 
struct an  amalgamated  series  out  of  the  two  estima- 
tions by  taking  for  each  pupil  the  mean  of  the  two 
rank-numbers  that  he  has  obtained  and  bringing  to- 
gether these  means  for  the  new  rank-order. 

Distinct  differences  in  method  will  appear  when 
the  estimation  of  intelligence  is  made  in  elementary 
schools  (Volksschule)  than  when  in  higher  schools. 

The  elementary  school  teacher  has  the  particular 
advantage  that  he  is  usually  the  only  teacher  of  the 
class,  and  thus  can  observe  the  behavior  of  the  chil- 
dren in  the  most  varied  activities,  in  technical  and 
theoretical  subjects,  at  play  and  at  work.  But  just 
this  very  breadth  of  information  also  renders  him  in 
a  certain  sense  less  independent  in  his  estimation. 
Because  his  knowledge  of  his  pupils  extends  in  so 
comprehensive  a  manner  over  their  school  perform- 
ances; all  their  grades  and  the  determination  of 
their  class-places  are  the  product  of  a  single  teacher, 
so  that  it  is  psychologically  easily  intelligible  that  he 
can  not  so  easily  free  himself  from  this  judgment 
that  he  has  himself  worked  out,  even  when  he  under- 


takes  the  entirely  different  problem  of  estimating 
their  intelligence. 

With  the  teacher  in  the  higher  schools  the  situa- 
tion is  different.  He  instructs  only  in  certain  sub- 
jects and  thus  comes  to  know  his  pupils  only  par- 
tially. This  certainly  renders  the  estimation  of  their 
intelligence  difficult.  The  departmental  teacher 
must  especially  guard  against  identifying  special 
talent  or  lack  of  talent  in  his  special  subject  with 
general  intelligence  or  the  lack  of  it.  Yet  he  is  less 
biassed  in  his  construction  of  a  rank-order  by  the 
same  circumstances,  in  that  the  rank-order  of  the 
school,  if  there  be  one,  is  never  his  own  work  that 
might  affect  his  judgment  by  auto-suggestion,  but  is 
something  that  has  been  obtained  by  the  mere  me- 
chanical addition  of  all  the  different  performances 
of  the  pupils,  including  performances  in  other  sub- 
jects with  which  he  has  nothing  to  do.  And  this  en- 
tails a  further  advantage,  viz.,  that  estimations  of 
the  intelligence  of  the  same  group  of  pupils  can  be 
obtained  from  the  different  departmental  teachers 
who  instruct  them,  and  that  these  estimations  can 
then  be  compared  with  each  other  and  finally  amal- 
gamated into  a  single  series.  Of  course,  for  the  pur- 
pose of  making  a  comparison  of  this  sort  only  those 
teachers  should  be  drawn  upon  whose  subjects  of  in- 
struction can  afford  a  basis  for  a  fairly  exact  knowl- 
edge of  the  pupils — not,  then,  some  teacher  who 
might  give  instruction  to  the  class  in  some  minor  ac- 
cessory subject  only. 

It  is  evident,  also,  that  teachers  can  be  asked  to 
make  estimations  of  their  pupils'  intelligence  only 
after  they  have  become  intimate  with  them — not,  for 


ESTIMATION  AND   TESTING  OF   FINER  GRADATIONS       127 

instance,  right  after  the  beginning  of  the  school  year. 
Teachers  that  have  accompanied  a  class  and  known 
them  more  than  a  single  year  supply  especially 
favorable  conditions  for  the  work. 

3.    Estimated  Intelligence  and  School  Performance 

These  theoretical  considerations  may  now  be  illus- 
trated by  a  series  of  quantitative  results  that  bear 
on  the  relation  between  estimated  intelligence  and 
school  performance.  I  shall  make  use  of  some  al- 
ready published  material  of  English  origin  and  also 
of  some  as  yet  unpublished  material  that  has  been 
gathered  as  opportunity  offered  by  members  of  the 
psychological  department  at  Breslau. 

In  the  English  investigations  (Table  XV)  the 
school  performance  has  been  measured  in  different 
ways;  in  some  there  were  used  the  class-places,  in 
others  the  results  of  school  examinations,  which  are 
held  regularly  in  all  classes  in  England.  Unfortu- 
nately, the  special  methodological  measures  that 
were  taken  in  securing  the  estimated  intelligence  are 
not  precisely  enough  reported  to  permit  us  to  pass 
any  judgment  concerning  the  reliability  of  the  re- 
sults. 

In  all  cases  there  are  clear,  and  in  some  high  cor- 
relations— decidedly  higher,  it  is  to  be  noted,  be- 
tween intelligence  and  the  results  of  examinations 
than  between  intelligence  and  class-place  (0.76  as 
compared  with  0.68).  This  result  is  not  without  in- 
terest. So  far  as  we  may  judge  from  the  account 
of  the  investigation,  the  estimation  of  intelligence 
had  been  undertaken  without  the  results  of  the  ex- 
aminations having  been  known — indeed,  in  some 


128    PSYCHOLOGICAL   METHODS  OF   TESTING   INTELLIGENCE 


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ESTIMATION  AND   TESTING  OP  FINER  GRADATIONS       129 

cases  before  these  had  taken  place.  The  estimates, 
then,  were  not  affected  by  the  ranking  in  the  school 
tests,  and  the  rather  high  correlation  could  therefore 
be  regarded  as  a  reliable  expression  of  the  degree  of 
correspondence  between  intelligence  and  the  work 
done  in  the  examinations.  Burt  also  had  estimates 
of  intelligence  of  the  same  pupils  made  by  different 
teachers  and  by  disinterested  school-mates  of  the 
pupils.  The  correlations  between  these  estimates 
are  very  high,  but  since  all  those  who  estimated  set 
out  from  the  already  known  rank-order  of  the  pupils, 
which  they  had  merely  to  correct,  it  follows  that  this 
high  correspondence  is  nothing  remarkable  and  that 
it  has  no  scientific  value. 

In  the  course  of  discussions  of  this  subject  in  the 
meetings  of  the  Psychological  Seminary  at  Breslau, 
during  the  winter  semester  1911-12,  the  need  became 
evident  of  clearing  up  the  methodological  aspects  of 
the  whole  subject  of  estimating  intelligence  by  trials 
of  our  own.  Fortunately,  two  of  our  members,  who 
were  engaged  in  practical  school  work,  were  ready  to 
secure  new  material.3  The  results  thus  obtained  are 
worth  noting  because  they  very  clearly  demonstrate 
the  methodological  difficulties  and  the  way  to  over- 
come them  and  also  bring  out  the  necessary  differ- 
ence between  the  procedure  in  secondary  and  in  ele- 
mentary schools. 

Principal  Rindfleisch  had  the  teachers  in  charge 
of  a  boys'  Volksschule  prepare  for  their  classes  lists 
that  showed  both  the  ranking  of  the  pupils  on  the 

'Hearty  thanks  are  due  to  Principal  Rindfleisch  (Liegnitz)  and 
Dr.  Scheifler  (a  high-school  teacher  at  Gorlitz)  for  their  great 
pains  and  for  their  courtesy  in  placing  the  material  at  my  disposal. 


130    PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

basis  of  their  performances  and  also  their  ranking 
according  to  their  intelligence.  So  far  as  it  has 
proved  feasible  I  have  calculated  the  rank-correla- 
tions of  these  lists.  It  must  be  stated  that  quite  a 
number  of  the  lists  had  to  be  excluded  ;  some  because 
the  teacher  had  been  satisfied  to  present  the  material 
arranged  in  a  very  few  intelligence-groups,  and  some 
because  the  necessary  precautions  of  method  had 
plainly  not  been  observed.  Thus,  there  were  many 
lists  that  showed  plainly  that  the  rank-order  for 
school  performances  had  been  arranged  first  and 
then  the  rank-order  for  intelligence  had  been  ar- 
ranged from  it  with  only  a  very  few  corrections. 

TABLE   XVI 
VOLKSCHUI-E  LIEGNITZ 

School  Number     Number 

Class        Year  Age  Tested      Omitted          Q        P.   E. 

Via  1.  6.3-7.6  47  8  0.85  -+.  0.05 

VIb  1.  6.0-7.1  37  16  0.78  -+-  0.07 

0.47  +  0.1 


Vb  2  7787 

*•  7-7'8-7          )  (34)  (13  (0.74  +  0.08) 

IVa  3.             8.3-10.0  "  45  13  0.87  -+-  0.05 

Ilia  4.             9.3-11.6  43  11  0.88  -+-  0.05 

Ila  5.  10.3-12.2  30  14  0.97  ±  0.03 

la  6.  11.6-13.6  30  12  0.91  -+-  0.05 

The  remaining  lists,  however,  cover  all  the  differ- 
ent school  grades.  The  important  data  are  shown  in 
Table  XVI.  There  it  will  be  noted  that  in  figuring 
the  correlation  I  left  out  in  each  class  a  number  of 
pupils  whose  age  exceeded  the  proper  limits.  If  we 
leave  Class  Vb  out  of  consideration  for  the  moment, 
the  correlations  are  then  uniformly  markedly  high  — 
between  .78  and  .97  ;  average  without  Class  Vb  = 
0.88.  The  fact  that  the  correlation  is  higher  than  the 


ESTIMATION  AND   TESTING  OF   FINER  GRADATIONS        131 

English  correlation  between  estimated  intelligence 
and  class-place  is  doubtless  due  to  the  circumstance 
that  the  English  were  content  to  use  a  small  number 
of  classificatory  groups  of  intelligence,  whereas  in 
our  lists  serial  ranking  was  required.  This  more  dif- 
ficult task  brought  out  a  somewhat  higher  depend- 
ence on  the  school  ranking,  which  was  known  by  the 
teachers  and  in  fact  prepared  by  them.  Hence  this 
very  high  correlation  is  not  a  proper  expression  of 
the  actual  degree  of  connection  between  intelligence 
and  school  work,  as  will  be  seen  more  clearly  upon  a 
closer  analysis  of  the  lists.  There  are  certain  symp- 
toms by  which  one  can  tell  very  positively  whether 
the  teacher  has  or  has  not  made  the  attempt  to  free 
himself  from  the  suggestive  influence  of  the  school 
ranking;  and  the  more  seriously  this  attempt  was 
made,  the  smaller  was  the  correlation. 

Mention  must  be  made  in  this  connection  of  the 
Class  Vb,  whose  teacher  plainly  undertook  the  work 
with  great  independence  and  with  fine  psychological 
comprehension.  This  teacher  settled  the  numbering 
for  his  intelligence  series  without  glancing  at  his 
school-work  series  and  sought  to  explain  the  cases 
of  special  discrepancy  between  school  performance 
and  intelligence  by  brief  remarks  ("  moved  in  from 
the  country,"  "sick  a  long  time,"  "poor  home  condi- 
tions, ' '  etc. ) .  The  result  was  astonishing — a  correla- 
tion of  only  0.47. 

This  one  correlation  is,  in  my  opinion,  psycholog- 
ically and  methodologically  more  important  than  the 
much  higher  ones  obtained  for  the  other  classes,  be- 
cause the  lack  of  higher  correlation  is  certainly  due 
not  to  any  peculiar  composition  of  the  Class  Vb,  but 


132   PSYCHOLOGICAL   METHODS   OF  TESTING   INTELLIGENCE 

to  the  special  care  and  capacity  for  judging  of  the 
teacher  who  did  the  estimating. 

I  have  made  a  further  calculation  for  this  Class 
Vb  by  excluding  those  six  pupils  in  whose  cases  there 
existed,  according  to  the  teacher's  notes,  special  con- 
ditions. The  correlation  for  the  remaining  34  then 
rose  at  once  to  0.74 ;  in  other  words,  it  approximated 
very  closely  the  lowest  correlations  computed  for  the 
other  classes.  From  this  it  follows  for  this  particu- 
lar class,  and  presumably  as  a  general  principle,  too, 
that  the  low  correlation  first  secured  is  not  due  to 
any  distinct  thorough-going  discrepancy  between  de- 
gree of  intelligence  and  school  efficiency,  but  rather 
to  an  unusual  discrepancy  between  endowment  and 
performance  in  a  minority  of  the  pupils.  This  small 
group  demands  the  special  consideration  of  the 
teacher  and  individual  treatment,  for  it  is  with  them 
that  the  danger  is  greatest  that  the  ordinary  valua- 
tion of  the  children  in  terms  of  their  school  work 
may  lead  to  an  erroneous  appraisement  and  han- 
dling. 

Turning  to  the  higher  schools,  I  have  at  my  dis- 
posal now  a  single  class  only,  but  the  estimation  of 
the  intelligence  of  this  class  has  special  value  on  ac- 
count of  the  great  thoroughness  and  j^^autions  of 
method  adopted,  and  on  account  of  thM^that  sev- 
eral teachers  joined  in  estimating  the  sflJF  children. 
Table  XVII  exhibits  the  correlations  that  I  have 
computed.  I  have  to  thank  the  regular  master  of  the 
class  for  the  material. 

The  class  was  an  Untertertia  grade  in  a  Gymna- 
sium.4 The  regular  teacher  (Teacher  A)  was  well 

'This  would  correspond  scholastically  approximately  to  our  first 
high-school  year. — Translator. 


ESTIMATION  AND   TESTING  OF  FINER  GRADATIONS       133 

trained  psychologically  and  as  a  member  of  my  semi- 
nary understood  perfectly  the  things  to  be  kept  in 
mind  in  estimating  intelligence.  As  he  had  already 
taught  these  pupils  the  year  before  and  had  given 
them  during  the  current  year  ten  hours  of  instruc- 
tion a  week  (Latin  and  French),  it  may  be  taken  for 
granted  that  he  possessed  a  really  exact  acquaint- 
ance with  the  material  before  him.  It  can  therefore 
be  said  that  his  estimation  of  their  intelligence  was 
made  under  specially  favorable  conditions.  More- 
over, he  had  two  otherteachers  estimate  the  same 
pupils.  Of  these,  Teacne^p  ;-it  is  true,  instructed  the 
class  only  two  hours  a  week  in  history  and  Teacher 
C  four  hours  a  week  in  religion  and  German.  The 
instructions  were  to  judge  the  children  not  on  the 
basis  of  the  particular  ability  that  they  might  have 
displayed  in  the  subjects  the  teachers  taught,  but  on 
the  basis  of  the  impression  of  their  general  intelli- 
gence. Beside  these  three  estimated  orders  there 
was  also  available  the  series  of  'class-places'  of  the 
pupils.  In  making  my  calculations  I  excluded  eight 
pupils  who  were  too  old.  There  remained  23 — 
enough  to  permit  the  reckoning  of  valid  correlations. 
Now  a  first  glance  at  the  table  shows  that  the  correla- 
tion between  intelligence  and  class-place  is  much 
lower  than  those  obtained  in  most  of  the  elementary 
school  classes.  The  specially  reliable  estimation  of 
Teacher  A  gives  a  correlation  of  0.43.  Of  those  for 
the  two  other  teachers,  the  one  is  somewhat  higher, 
the  other  somewhat  lower.  When  we  combine  the 
estimates  of  all  three  teachers  into  an  amalgamated 
estimation-series,  we  obtain  again  a  correlation  with 
the  class-place  of  0.45 — a  value  that  coincides  almost 


134   PSYCHOLOGICAL   METHODS   OF  TESTING   INTELLIGENCE 

exactly  with  that  of  the  single  elementary  class  Vb 
that  we  have  accorded  special  treatment.  Hence  it 
appears  that  when  an  estimation  of  intelligence  is 
made  with  special  thoroughness  and  caution,  there 
exists  only  a  moderate  degree  of  correlation  between 
it  and  school  efficiency. 

TABLE  XVII 

Class:  U  III  of  a  Gymnasium  (7th  school  year). 

Ages  of  those  investigated :  13.5  to  14.5  years. 

Number  investigated:  23  (8  others  omitted  as  too  old). 

Number  of  teachers  estimating:  3  (Teacher  A  the  principal 
teacher). 

Correlations  between  estimated  intelligence  and  class-place : 

Teacher  A  and  Class-Place 0.43  -+-  0.13 

Teacher  B  and  Class-Place 0.55  -+-  0.12 

Teacher  C  and  Class-Place 0.33  -j-  0.14 

Teachers  B  and  C  (combined)  and  Class-Place 0.49  -+-  0.13 

Teachers  A,  B  and  C  (combined)  and  Class-Place. . . .     0.45  -j-  0.13 

Intercorrelations  of  the  Estimations : 

Teacher  B  and  Teacher  A 0.69  -+-  0.10 

Teacher  C  and  Teacher  A 0.65  -j-  0.12 

Teachers  B  and  C  (combined)  and  Teacher  A 0.75  -j-  0.10 

The  values  obtained  for  all  three  of  the  secondary 
school  teachers  alike  show  that  it  is  much  easier  for 
the  individual  teacher  in  the  secondary  school  to  rid 
himself  from  the  influence  of  the  class  arrangement, 
because  this  arrangement  has  not  been  determined 
by  himself  alone. 

The  reliability  of  the  result  is  augmented  by  the 
inter  cor  relation  of  the  series  of  the  teachers.  These 
correlations  are,  in  fact,  much  higher :  highest  (0.75) 
when  the  estimates  of  the  two  supplementary  teach- 
ers are  combined  and  related  to  the  particularly 
trustworthy  estimate  of  the  regular  class-teacher. 
That  is  to  say,  then,  the  estimation  of  intelligence  un- 
dertaken by  the  teachers  quite  independently  of  one 
another  exhibit  a  great  similarity  to  one  another, 


ESTIMATION  AND  TESTING  OF  FINER  GRADATIONS       135 

despite  the  fact  that  the  several  teachers  derived 
their  judgments  from  observations  in  quite  different 
school  subjects.  This  decided  correspondence  of  the 
judgments  of  the  teachers  on  their  pupils'  intelli- 
gence, taken  in  conjunction  with  the  fair  degree  of  in- 
dependence of  their  judgment  from  the  class-place, 
seems  to  me  to  be  a  forcible  argument  for  the  scien- 
tific usefulness  of  the  method  of  intelligence  estima- 
tion. But  the  result  also  teaches  us,  when  we  com- 
pare with  it  the  experience  gained  in  the  elementary 
school,  that  only  such  estimations  of  intelligence  are 
useful  as  have  been  carried  out  by  an  exact  method 
and  with  special  psychological  knowledge. 

4.    Rank-orders  of  Intelligence  obtained  by  Tests 

We  can  now  return  once  more  to  the  starting  point 
of  this  whole  section,  the  experimental  testing  of  in- 
telligence. For  we  may  safely  regard  the  estimation 
of  intelligence  by  the  teachers,  when  undertaken  with 
the  necessary  precautions,  as  a  suitable  control-de- 
vice by  which  we  can  measure  the  reliability  of 
experimental  testing. 

The  material  just  now  available  on  the  correlation 
between  rank-orders  obtained  by  tests  and  those  ob- 
tained by  estimations  is,  to  be  sure,  very  scanty,  yet  it 
is  already  enough  to  indicate  the  direction  in  which 
greater  results  are  to  be  looked  for.  Here,  too,  do 
we  come  upon  that  principle  that  we  found  univer- 
sally applicable  in  intelligence  testing :  no  single  test 
of  whatever  kind,  but  only  a  skillfully  combined  sys- 
tem of  tests  yields  a  reliable  gradation  of  intelligence. 

Burt  in  England  and  Eies  in  Germany  have  car- 
ried on  with  normal  children  investigations  pertain- 


ing  to  this  field.  Burt  deals  with  but  a  small  number 
of  cases: — one  group  of  30  'elementary'  school- 
pupils  and  another  of  13  'secondary'  pupils ;  Eies  has 
investigated  five  classes  in  an  elementary  school. 
The  very  much  more  extensive  and  precise  investiga- 
tions of  the  Breslau  teacher,  Hylla,  have  unfortu- 
nately not  yet  been  completed. 

Burt  (72)  tested  his  classes  with  12  different  tests. 
The  rank-orders  obtained  for  the  different  tests  show 
quite  different  correlations  with  the  estimated  rank- 
order — six  tests  over  0.50,  six  tests  under  0.50.  The 
tests  that  show  the  higher  correlations  are  mostly 
those  that  pertain  to  attention,  motor  skill  and  mem- 
ory. These  tests  and  their  correlations  are  shown  in 
Table  XVIII.  On  the  other  hand,  the  tests  of  dis- 
criminative sensitivity  uniformly  show  very  low  cor- 
relations with  intelligence — a  result  worthy  of  note 
because  there  still  prevails  a  tendency  in  many  quar- 
ters to  use  sensory  tests  for  testing  intelligence. 

TABLE  XVIII 
BUBT'S    EXPEBIMENTS    WITH    NOBMAL   CHILDBEN 

r-Correlation  with-> 

Est.  Intell. 
Elem.  Secndry 

Test  School  School 

1.  Dotting.    (A  zig-zag  row  of  dots  traveling 

at  constant  speed  must  be  hit  with  a 

pencil) 0.60  0.84 

2.  Spot  pattern.     (A  group  of  dots  to  be  re- 

produced by  drawing  after  5  exposures 

in  a  tachistoscope) 0.76  0.75 

3.  Mirror.    (A  pattern  visible  only  in  a  mir- 

ror is  to  be  pierced  at  marked  points) .     0.67  0.54 

4.  Memory  span  for  concrete  and  abstract 

words  and  nonsense  syllables 0.57  0.78 

5.  Alphabet.    (Cards  with  the  letters  of  the 

alphabet  are  to  be  properly  arranged) .     0.61  0.80 

6.  Sorting   (50  playing  cards  of  5  different 

colors  are  to  be  sorted  into  5  packs) . . .    0.52  0.56 

Resulting  rank-order  for  all  6  tests 0.85  0.91 


ESTIMATION  AND   TESTING   OP  FINER  GRADATIONS        137 

The  correlations  found  by  Burt  are  in  general 
somewhat  lower  for  the  elementary  than  for  the 
higher  school,  but  no  particular  value  is  to  be 
ascribed  to  the  higher  correlations  on  account  of  the 
small  number,  13,  of  subjects  in  the  second  group. 

Ries5  used  two  methods:  Method  A  is  patterned 
after  the  Banschburg  method  of  word-pairs;  each 
word-pair  is  comprised  of  two  words  that  stand  in  a 
causal  relation  to  one  another,  e.  g.,  'hunger* — 'weak- 
ness.' Each  pair  was  pronounced  and  their  reten- 
tion tested  by  the  method  of  right  associates.  Method 
B  was  in  the  form  of  an  association  experiment:  to 
each  word  pronounced  there  was  to  be  given  as  a 
response  a  word  whose  meaning  stood  in  the  relation 
of  effect  to  cause  with  the  stimulus  word.  In  both 
methods  the  plan  was  to  bring  intelligence  into  action 
by  the  use  of  logical  relations.  And  in  fact  the  re- 
sults did  furnish  a  very  high  correlation  with  esti- 
mated intelligence  and  with  a  small  probable  error, 
viz. :  with  Method  A  0.59,  0.85,  0.89,  0.86  and  0.90  (in 
the  different  classes)  and  with  Method  B  0.85,  0.94, 
0.86,  0.91. 

A  supplementary  test  undertaken  for  comparative 
purposes  by  means  of  the  Ebbinghaus  completion 
method  gave  in  two  classes  somewhat  smaller  cor- 
relations. 

Ries'  results  doubtless  show  that  the  methods  that 
he  proposes  may  lay  claim  to  a  place  in  a  system  of 
tests  for  securing  rank-orders  of  intelligence.  On 
the  other  hand,  it  should  not  be  concluded  from  the 


"Reference  78.    See  also  the  extensive  critical  review  of  Ries  by 
Bobertag,  Zeits.  f.  angew.  Psych.,  5,  p.  207. 


138    PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

high  correlations  that  Method  A  or  Method  B  taken 
alone  are  adequate  for  testing  and  ranking  intelli- 
gence. For,  in  the  first  place,  Ries'  results  do  not 

TABLE  XIX 

Ries'  experiments  on  24  boys  (Mittelschule,  2d  class,  ages  12-14). 

Test  A :    Method  of  word-pairs  and  right  associates. 

Test  B :    Association  of  effect  to  a  given  cause. 

Correlation  of  Test  A  with  Test  B 0.61 

Correlation  of  Test  A  with  Estimated  Intelligence 0.85 

Correlation  of  Test  B  with  Estimated  Intelligence 0.94 

Correlation  of  Tests  A  and  B  (combined)  with  Est  Int 0.98 

present  the  requisite  uniformity  (in  one  class, 
Method  A  correlated  with  estimated  intelligence  by 
only  0.59),  and  it  is  very  questionable  whether  repe- 
tition of  the  tests  in  other  places  would  furnish  the 
same  high  correlations.  Again,  each  of  his  methods 
tests  only  one  phase  of  intelligence,  and  a  comparison 
of  the  two  methods  with  one  another  shows  how  little 
right  we  have  to  infer  one  phase  from  the  other. 
Thus,  Eies  gives  for  one  class  a  table  of  the  original 
data  from  which  I  have  been  able  to  calculate  some 
results  not  mentioned  by  him  (Table  XIX).  The  re- 
sult is  that  the  two  methods  do  not  correlate  at  all 
highly  with  one  another,  only  0.61 ;  in  other  words, 
the  ranking  of  intelligence  by  Method  A  furnishes  a 
distribution  of  stations  that  is  in  some  parts 
quite  different  from  the  distribution  furnished  by 
Method  B. 

The  example  is,  however,  excellently  adapted  to 
point  out  the  way  toward  the  method  that  is  to  be  ap- 
plied. 

What  does  it  mean  that  both  tests  correlate  so  high 
with  estimated  intelligence,  but  so  low  with  one  an- 


ESTIMATION  AND  TESTING  OF   FINER  GRADATIONS       139 

other  ?  Plainly,  this  is  possible  only  when  the  rank- 
orders  obtained  by  the  tests  deviate  from  the  rank- 
order  obtained  by  estimation  in  contrary  directions 
in  some  portions  of  the  series. 

In  illustration :  if  a  pupil  obtains  Station  10  in  the 
estimated  rank-order,  Station  8  in  the  order  of  Test 
A  and  Station  12  in  the  order  of  Test  B,  and  if  a  simi- 
lar thing  occurs  with  other  pupils,  then  the  above- 
mentioned  differences  in  the  correlations  follow  of 
necessity.  But  it  is  equally  evident  that  the  combin- 
ing of  the  two  stations  for  tests,  8  and  12,  gives  the 
so-called  "resulting  rank-place  for  tests,"  10,  a  value 
that  now  coincides  with  the  station  for  estimated 
rank-order.  The  two  tests  therefore  mutually  com- 
pensate one  another  and  thus  form,  when  combined, 
a  measure  of  intelligence  that  comes  much  nearer 
the  estimated  intelligence  than  either  test  by  itself. 
Put  psychologically,  the  tests  demand  the  activity  of 
aspects  of  intelligence  so  different  as  to  be  very  un- 
equally developed  in  one  and  the  same  person,  but 
which,  taken  together,  do  characterize  his  degree  of 
intelligence. 

And,  as  a  matter  of  fact,  the  correlation  computed 
from  Eies'  data  did  figure  out  so  that  the  amalga- 
mated rank-order  for  the  two  tests  presents  the  ex- 
traordinarily high  correlation  with  estimated  intelli- 
gence of  0.98. 

In  this  way,  then,  the  mutual  compensation  of  tests 
that  we  have  already  set  forth  as  a  requirement,  be- 
comes a  controlling  principle  of  the  test-series,  and 
the  correlation  method  gives  us  a  numerical  device 
for  discovering  that  combination  of  tests  in  which  we 
approach  most  nearly  to  perfect  compensation.  I 


140    PSYCHOLOGICAL    METHODS  OF   TESTING   INTELLIGENCE 

mean  that  we  must  combine  together  tests  that  cor- 
relate less  with  one  another  than  each  one  of  them 
correlates  with  estimated  intelligence,  and  that  com- 
bination whose  amalgamated  rank-order  shows  the 
highest  and  most  constant  correlation  with  estimated 
intelligence  is  the  system  of  tests  that  we  seek.  Nat- 
urally, we  shall  not  limit  ourselves  to  two  tests  in 
making  our  system,  but  shall  combine  a  larger  num- 
ber into  one  compensation-system. 

This  was  the  idea  that  incited  Hylla  to  the  investi- 
gations previously  mentioned  which  are  still  in  prog- 
ress. The  idea  of  compensation  as  a  principle  in  as- 
sembling tests  has  already  arisen  simultaneously 
both  in  England  and  in  France. 

Thus,  from  the  tests  that  had  afforded  the  highest 
correlations  with  estimated  intelligence  in  his  in- 
vestigations, Burt  worked  out  an  amalgamated  rank- 
order  whose  correlation  with  estimated  intelligence 
considerably  exceeded  all  the  single  correlations 
(Table  XVIII).  In  the  elementary  school  the  single 
correlations  ranged  between  0.52  and  0.76,  that  of 
their  combination  amounted  to  0.85;  in  the  higher 
schools  the  single  correlations  ranged  between  0.54 
and  0.84,  while  the  correlation  for  the  combined  tests 
rose  to  0.91.  From  this  Burt  draws  the  conclusion 
(pp.  158-9) :  "By  means,  then,  of  some  half-dozen 
tests,  we  are  able  independently  to  arrange  a  group 
of  boys  in  an  order  of  intelligence,  which  shall  be  de- 
cidedly more  accurate  than  the  order  given  by 
scholastic  examination,  and  probably  more  accurate 
than  the  order  given  by  the  master,  based  on  personal 
intercourse  during  two  or  three  years,  and  formu- 
lated with  unusual  labor,  conscientiousness  and 
care." 


ESTIMATION   AND   TESTING  OF  FINER  GRADATIONS        141 


This  conclusion  sounds  extremely  optimistic  in- 
deed, since  the  material  that  Burt  had  at  his  disposal, 
43  subjects,  does  not  in  the  slightest  degree  suffice 
for  the  formulation  of  such  a  thesis.  However,  the 
principle  that  it  embodies  is  so  promising  and  so  il- 
luminating as  imperatively  to  demand  a  thorough  re- 
testing  by  the  most  exact  methods  and  on  a  very  ox- 
tensive  scale. 

An  analogous  result  has  been  found  also  with 
feeble-minded  children.  Mile.  Descoeudres  (73) 
tested  14  children  in  an  institution  by  means  of  15 
different  tests.  It  is  true  that  the  children  differed 
very  greatly  in  age  (from  6.5  to  14  years),  yet  it  was 
possible  to  estimate  their  intelligence  by  the  general 
impression  that  they  made  in  the  house  and  in  the 

TABLE   XX 
DESCOEUDRES  :     EXPERIMENTS  ON  FEEBLE-MINDED   CHILDREN 

r-Correlat'ns  with  Estlntell.-^ 

of  all 

of  each      of  each     the  tests 
5  tests      combined 


Tests  test 

1.  Comparison  of  terms 0.878 

2.  Computation 0.868 

3.  Describing   pictures 0.842 

4.  Problem-questions 0.817 

5.  Tactual  discrimination 0.812 

6.  Definitions 0.801 

7.  Stringing   beads 0.780 

8.  Inventiveness     (a     picture    is 

shown :  what  are  the  persons 

in  it  talking  about?) 0.761 

9.  'Patience'    (restoring   a   cut-up 

picture) 0.734 

10.  Knowing  four  coins 0.699 

11.  Attention  (cancelling  a's) 0.671 

12.  Visual  memory  (5  objects) 0.646 

13.  Noting  omissions  in  drawings.  0.637 

14.  Auditory  memory   (5  words) . .  0.539 

15.  Naming  60  words  in  3  min 0.509 


0.91 


0.84 


0.73 


0.99 


142   PSYCHOLOGICAL   METHODS  OF  TESTING   INTELLIGENCE 

schoolroom  and  to  arrange  them  in  order  on  this 
basis.  The  first  column  of  figures  in  Table  XX  shows 
the  correlations  of  the  several  tests  with  the  esti- 
mated rank-order.  The  correlations  are  arranged  in 
order  of  their  magnitude  and  run  from  0.88  to  0.51. 
Mile.  Descoeudres  also  calculated  the  amalgamated 
rank- order  for  all  the  tests  and  found  a  correlation 
of  0.99  between  it  and  estimated  intelligence — almost 
complete  correspondence,  then,  between  the  two  se- 
ries. I  have  not  myself  checked  up  this  value  to  see 
if  it  is  absolutely  correct,  but  I  have  from  the  original 
data  calculated  the  correlation  with  intelligence  for 
each  5  tests,  taken  in  combination  (Column  2)  and  in 
each  case  I  found  confirmation  of  the  rule  that  the 
amalgamated  correlation  was  considerably  higher 
than  the  highest  correlation  of  any  single  one  of  the 
tests  of  which  it  was  compounded. 

A  few  hints  may  be  added  concerning  certain  other 
points  to  be  observed  in  working  at  the  problem  of 
ranking  by  tests. 

(a)  Measur ability.    It  must  be  possible  to  ex- 
press the  performance  in  the  test  conveniently  and 
unequivocally  by  a  numerical  value :  and  these  numer- 
ical values  must  make  sufficient  differentiation  with- 
in a  group  that  a  rank-order  of  performance  can  be 
drawn  up. 

(b)  Reliability.    A  test  is  reliable  only  when  its 
outcome  is  a  true  expression  of  abilities  and  is  not  too 
much  affected  by  variable  and  temporary  conditions. 
Reliability  is  tested  by  applying  the  same  (or  an 
analogous)  test  several  times  to  the  same  group  of 
subjects.    Only  if  these  repeated  testings  show  a  high 
degree  of  intercorrelation  is  the  test  valid  scientific- 
ally. 


ESTIMATION  AND   TESTING   OF  FINER  GRADATIONS       143 

(c)  Fairly  high  correlation,  even  of  the  single 
test,  with  estimated  intelligence.    Because  tests  that 
of  themselves  exhibit  little  or  no  relation  to  intelli- 
gence can  not,  of  course,  gain  symptomatic  signifi- 
cance for  intelligence  by  combination,  however  many 
of  them  are  combined. 

(d)  Comprehensiveness  of  the  tests,  and  that  in 
two  directions.    First,  we  should  endeavor  to  bring 
into  action  the  different  functions  concerned  in  intel- 
ligence (see  above,  pp.  20  f.).    Secondly,  we  should 
take  care  that  the  numerical  records  refer  not  only  to 
quantity,  but  also  to  the  quality  of  the  performance, 
e.  g.,  both  to  the  number  of  units  accomplished  in  a 
given  time  and  also  to  the  percentage  of  errors  made 
during  the  work. 

(e)  We  should  see  to  it  that  the  estimation  of  in- 
telligence be  done  thoroughly  and  conscientiously. 

(/)  When  a  considerable  number  of  tests  have 
been  carried  out  upon  a  group,  then  combine  the  re- 
sults into  different  amalgamated  rank-orders  until 
that  combination  has  been  found  that  yields  the 
strongest  correlation  with  the  estimated  intelligence. 
The  combination  should  then  be  tested  out  on  other 
groups. 

The  construction  of  an  amalgamated  rank-order  is 
very  easy.  The  ranks  obtained  by  each  subject  in  the 
several  tests  are  combined  into  an  average  value. 
These  average  values  themselves  do  not  form  the  se- 
ries desired,  but  must  first  be  revised  into  ordinal 
numbers  that  represent  the  final  rank-order. 

Example :  The  pupils  have  been  tested  in  three  tests.  The  best 
pupil  has  obtained  in  the  three  trials  the  rank-places  3,  1,  1,  the 


144   PSYCHOLOGICAL    METHODS   OP   TESTING   INTELLIGENCE 

second-best  the  places  1,  2,  4,  the  third  the  places  2,  4,  2,  etc.    The 

3+1+1  1+2+4 

averages  are  for  Pupil  A  —L-^--  =  1.67,  for  B     ^g       =  2.33, 

2+4+2 
for  C  3 —  =  2.67.    Hence,  in  the  final  or  amalgamated  series, 

A  receives  the  Rank-place  1,  B  Place  2,  C  Place  3. 

If  we  proceed  in  this  manner  we  may,  I  think,  ex- 
pect that  the  method  of  amalgamated  ranks  can  be 
worked  out  into  a  systematized  plan  of  procedure,  as 
has  already  been  done  with  the  method  of  age-levels. 

Not  until  we  combine  both  these  ideas  can  we  hope 
to  master  the  whole  field  of  intelligence  testing.  The 
system  of  levels  draws  the  great  wave-lines  of  mental 
development:  the  method  of  ranking  sketches  the 
finer  ripples  within  each  level,  and  in  such  a  manner 
that  the  precise  evaluation  of  the  degree  of  intelli- 
gence of  the  individual  child  shall  be  possible.  At  the 
same  time,  the  purely  psychological  analysis  of  the 
behavior  of  the  subject  toward  the  test  must  not  be 
neglected,  because  it  supplements  the  quantitative  de- 
termination of  intelligence  by  making  it  possible  to 
ascertain  the  qualitative  'coloring'  of  the  intelligence 
in  the  individual  case. 


BIBLIOGRAPHY 


BIBLIOGRAPHY. 

The  following  abbreviations  are  used : 

AmJPs  =.  American  Journal  of  Psychology. 

AnPs  =  L'Annee  psychologique. 

ArdePs  =  Archives  de  psychologie. 

BrJPs  =  British  Journal  of  Psychology. 

EPd  =  Die  experimentelle  Padagogik. 

JEdPs  =  Journal  of  Educational  Psychology. 

JNeMeDis  =  Journal  of  Nervous  and  Mental  Diseases. 

JPsAsth  =  Journal  of  Psycho- Asthenics. 

PdSe  =  Pedagogical  Seminary. 

PsCl  =  Psychological  Clinic. 

PsMon  =  Psychological  Monographs  (Review  Pub.  Co.). 

TrSc  =  The  Training  School. 

ZAngPs  =  Zeitschrift  fur  angewandte  Psychologie. 

ZEPd  =  Zeitschrift  fur  experimentelle  Padagogik. 

ZNPt  =  Zeitschrift  fur  die  gesamte  Neurologic  und  Psychiatric. 

ZPdPs  =  Zeitschrift  fiir  padagogische  Psychologie. 

ZPs  =  Zeitschrift  fUr  Psychologie. 

A  fairly  complete  bibliography  of  intelligence  testing  up  to  the 
summer  of  1911  will  be  found  in 

1.  W.  Stern.  Die  differentielle  Psychologie  in  ihren  methodischen 
Grundlagen.    Leipzig,  1911. 

On  this  account  we  give  in  the  bibliography  that  follows  only  the 
together  with  all  the  publications  that  are  not  contained  in  the 
earlier  list  (designated  by  an  asterisk).  The  starred  references, 
then,  save  for  a  few  additions,  represent  the  rich  productivity  of 
the  last  year  (summer  of  1911  to  September  of  1912). 

A.    On  the  Introduction  and  Part  I. 
( Single  Tests  and  Series  of  Tests. ) 

See  also  literature  cited  in  Reference  1,  pp.  426-431. 

2.  A.  Binet.    Attention  et  adaptation.    AnPs,  6 :  1900,  248-404. 
*3.    A.  Binet.    A  propos  de  la  inesure  de  1'intelligence.    AnPs, 

11 :    1905,  69-82. 

4.  M.  Dosai-Revesz.     Exp.  Beitrag  z.  Psychol.  der  moralisch 
verkommenen  Kinder.    ZAngPs,  5 :  1911,  272-330. 

5.  H.   Ebbinghaus.     Ueber   eine  neue  Methode  zur   Prtifung 
geistiger  Fahigkeiten  u.  ihre  Anwendung  bei  Schulkindern.    ZPs, 
J3 :  1897,  401-459. 

147 


148   PSYCHOLOGICAL   METHODS   OP   TESTING   INTELLIGENCE 

*6.  S.  I.  Franz.  Handbook  of  mental  examination  methods. 
JNeMeDisMon  No.  10,  1912.  Pp.  165. 

*7.  W.  Healy  and  G.  M.  Fernald.  Tests  for  practical  mental 
classification.  PsMon,  1911.  No.  54.  Pp.  53. 

8.  K.  Heilbronner.  Zur  klinisch-ps.  Untersuchungstechnik. 
Monatsschrift  f.  Psychiatric,  17:  1905,  117-132. 

*9.  E.  B.  Huey.  Backward  and  feeble-minded  children. 
EdPsMon,  1912. 

*10.  E.  B.  Huey.  Retardation  and  the  mental  examination  of 
retarded  children.  JPsAsth,  15 :  1910,  31-43. 

11.  Intelligenzproblem  und  Schule.     Bericht  iiber  den  zweiten 
Verhandlungstag  des  I.  Kongresses  f.  Jugendbildung  u.  Jugend- 
kunde  zu  Dresden,  Oct.,  1911.    Arbeiten  des  Bundes  f.  Schulreform, 
5 :  1911. 

12.  K.  Jaspers.    Die  Methoden  der  Intelligenzprufung  und  der 
Begriff  der  Demenz.  Krit.  Referat.    ZNPt,  Ref.  1,  1910,  401-452. 

*12a.  R.  H.  Johnson  and  J.  Gregg.  Three  new  psychometric 
tests.  PdSe,  19 :  1912,  201-203. 

*12b.  Kurtze.  Intelligenzpriifung.  Zeits.  f.  Beh.  Schwachsinn., 
32 :  1912,  69-79. 

*13.  O.  Lipmann.  Katalog  der  Ausstellung  des  Inst.  f.  ang.  Ps. 
u.  ps.  Sammelforschung.  Bericht  iiber  den  V.  Kong.  f.  exp.  Ps.  in 
Berlin.  1912. 

14.  E.  Meumann.     Intelligenzpriifung  an  Kindern  der  Volks- 
schule.    EPd,  1 :  1905,  35-100. 

15.  E.  Meumann.     Der  gegenwartige  Stand  der  Methodik  der 
Intelligenzpriifung.    ZEPd,  11 :  1910,  68-79. 

*16.  E.  Meumann.  Ueber  eine  neue  Methode  der  lutelligenzprii- 
fung  und  iiber  den  Wert  der  Kombinationsmethoden.  ZPdPS,  13 : 
1912,  145-163. 

*17.  Meyer.  Die  Bedeutung  der  modernen  Psychologie  f.  d. 
Militarwesen.  Neue  Militar.  Blatter.  1911,  53  Jahrg.,  Nos.  6,  9, 10. 

*18.  Meyer.  Psychologie  und  militarische  Ausbildung.  ZPdPs, 
13  (2),  81-85. 

19.  H.  Miinsterberg.  Finding  a  life  work.  McClure's  Mag., 
1910,  398-403. 

*20.  H.  Munsterberg.  Experimentalpsychologie  und  Berufs- 
wahl.  ZPdPs,  13 :  1912,  1-7. 

*21.  O.  S.  Myers.  The  pitfalls  of  'mental  tests.'  Brit.  Med. 
Jour.,  28,  I,  1911.  (Also  in  German  by  Bobertag,  ZAngPs,  6  (1), 
60-65.) 

22.  E.   Rodenwalt.     Aufnahmen  des   geistigen   Inventars   Ge- 
sunder  als  Massstab  fur  Defektpriifungen  bei  Kranken.    Monats- 
schrift f.  Psychiatric,  17 :  Erganzungsheft,  1905,  17-84. 

23.  G.  Rossolimo.    Allgemeine  Characteristik  der  ps.  Profile,  1. 
Geistig-minderwertige  Kinder,  2.  Nerven-  und  Geisteskranke.    Mos- 
cow, 1910.    Pp.  106. 

24.  G.  Rossolimo.    Psychologische  Profile.    Die  Methodik.    Mos* 
cow,  1910.    Pp.  52. 


BIBLIOGRAPHY  149 

*24a.  G.  Rossolimo.  Die  ps.  Profile.  Zur  Methodik  der  quanti- 
tativen  Untersuchung  der  psychischen  Vorgange  in  normalen  und 
pathol.  Fallen.  Kltnik  f.  ps.  Krankheiten,  6:  1911  (3),  46;  (4),  32. 

25.  S.  de  Sanctis.  Typen  und  Grade  mangelhafter  geistiger 
Entwicklung.  Eos,  2 :  1905,  97-115. 

*26.  R.  Sommer.  Ueber  die  Methoden  der  Intelligenzprufung. 
Klinik  f.  psychol.  u.  nerv.  Krankh.,  7 :  1912,  1-21. 

27.  J.  van  der  Torren.    Ueber  das  Auffassungs-  und  Unterschei- 
dungsvermb'gen  f.  optische  Bilder  bei  Kindern.    ZAngPs,  1 :  1908, 
189-232. 

28.  G.  M.  Wbipple.    Manual  of  mental  and  physical  tests.    Bal- 
timore, 1910.    2d  ed.,  1914. 

*29.  Mary  T.  Whitley.  An  empirical  study  of  certain  tests  for 
individual  differences.  Archives  of  Psychol.,  19.  New  York,  1911. 
Pp.  146. 

30.  T.  Ziehen.  Die  Prinzipien  und  Metboden  der  Intelligenz- 
prufung. Berlin,  1908.  3d  ed.,  1911.  Pp.  94. 

B.    On  Part  II. 

(Binet-Simon  Method.) 

See  also  literature  cited  in  Reference  1,  pp.  431-432. 

*31.  L.  P.  Ayres.  Tbe  Binet-Sinion  measuring  scale  for  intelli- 
gence. Some  criticisms  and  suggestions.  PsCl,  5 :  1911,  187-196. 

*32.  J.  C.  Bell.  Recent  literature  on  the  Binet  tests.  JEdPs, 
3 :  1912,  101-110. 

33.  Binet  and  Simon.  Le  developpement  de  1'intelligence  chez 
les  enfants.  AnPs,  14 :  1908,  1-94. 

*34.  A.  Binet.  Sur  la  necessity  d'une  methode  applicable  au 
diagnostic  des  arrieres  militaires.  Annales  med.-psych.,  Jan. -Feb., 
1910. 

35.  A.   Binet.     La  rnesure  du  developpement  de  1'intelligence 
chez  les  jeunes  enfants.    Bull,  de  la  soc.  libre  pour  l'6tude  ps.  de 
I'enfant.    Paris,  1911,  Nos.  10  and  11,  pp.  187-248. 

36.  Binet  et  Simon.     Nouvelles  recherches  sur  la  mesure  du 
niveau  intellectuel  chez  les  enfants  d'ecole.    AnPs,  17:  1911,  145- 
201. 

*37.  A.  Binet.  Die  neuen  Gedankeu  iiber  das  Schulkind.  Bearb. 
v.  G.  Anschutz  und  W.  J.  Ruttmann.  Leipzig,  1912.  Pp.  289. 

*38.  E.  Bloch  und  Anna  Preiss.  Ueber  Intelligenzpriifung  an 
normalen  Volksschulkindern  nach  Bobertag  (Methode  Binet- 
Simon).  ZAngPs,  6:  1912,  539-547.  (Cf.  notes  at  the  end.) 

39.  O.  Bobertag.    Binets  Arbeiten  iiber  die  intellektuelle  Ent- 
wicklung des  Schulkindes.    ZAngPs,  3 :  1909,  230-259. 

40.  O.  Bobertag.     Ueber  Intelligenzprufung.     I.     Methodik  und 
Ergebnisse  der  einzeluen  Tests.     ZAngPs,  5:  1911,  105-203.     II. 
Gesamtergebnisse  der  Methode.     ZAngPs,  6:  1912,  495-538.     (Cf. 
notes  at  the  end. ) 


150    PSYCHOLOGICAL   METHODS   OF   TESTING   INTELLIGENCE 

*41.  O.  Bobertag.  Intelligenzpriifungen  an  Schulkindern.  Die 
Grenzboten,  70 :  1911,  375-384. 

*42.  O.  Bobertag.  Quelques  reflexions  m6thodologiques  &  pro- 
pos  de  Techelle  metrique  de  Binet  et  Simon.'  AnPs,  18 :  1912,  271- 
288. 

*43.  F.  Chotzen.  Die  Bedeutung  der  Intelligenzprufungmethode 
von  Binet-Simon  f.  d.  Hilfsschule.  Die  Hilfsschule,  5 :  1912,  pp.  10. 

*44.  F.  Chotzen.  Die  Intelligenzprufungmethode  von  Binet- 
Simon  bei  schwachsinnigen  Kindern.  (Unter  Mitwirkung  von  Dr. 
M.  Nicolauer.)  ZAngPs,  6:  1912,  411-494.  (Cf.  notes  at  the  end.) 

45.  O.  Decroly  et  J.  Degand.  La  mesure  de  1'intelligence  chez 
les  enfants  normaux  d'apres  les  tests  de  MM.  Binet  et  Simon. 
Nouvelle  contribution  critique.  ArdePs,  9 :  1910,  81-108. 

*46.  A.  Descoeudres.  Les  tests  de  Binet  et  Simon  et  leur  valeur 
scolaire.  ArdePs,  11 :  1911,  331-350. 

47.  H.    H.    Goddard.      Four    hundred   feeble-minded   children 
classified  by  the  Binet  method.    PdSe,  17 :  1910,  387-397. 

48.  H.  H.  Goddard.    Two  thousand  normal  children  measured 
by  the  Binet  measuring  scale  of  intelligence.    PdSe,  18 :  1911,  232- 
259. 

49.  H.  H.  Goddard.    Die  Untersuchung  d.  Intellekts  schwach- 
sinniger  Kinder.    Eos,  6 :  1909,  177-197. 

*50.  Clara  H.  Town.  The  Binet-Simon  scale  and  the  psychol- 
ogist. PsCl,  5 :  1912,  239-244. 

*51.    A.  Jeronutti.    Rivista  pedagogica,  3 :  1909,  No.  3. 

*52.  Katherine  L.  Johnston.  An  English  version  of  Binet's 
tests  for  the  measurement  of  intelligence.  Training  College  Rec- 
ord, Nov.,  1910. 

*53.  E.  A.  Kirkpatrick.  The  Binet  tests  and  mental  ability. 
JEdPs,  3 :  1912,  337. 

54.  F.  Kramer.  Die  Intelligenzprufung  bei  kriminellen  und 
psychopathischen  Kindern.  Vortrag,  1911.  (See  Reference  11.) 

*55.  I.  Lawrence.  A  study  of  the  Binet  definition  tests.  PsCl, 
5 :  1911,  207-216. 

*56.  I.  B.  MacDonald.  The  Binet  tests  in  a  hospital  for  the 
insane.  TrSc,  7 :  1910. 

*57.  M.  Morl6.  L'influence  du  milieu  social  sur  le  degr6  de 
1'intelligence  des  enfants.  Bull,  de  la  soc.  libre,  etc.  12 :  1911, 
No.  1. 

*58.  Clara  Schmitt.  The  Binet-Simon  tests  of  mental  ability. 
Discussion  and  criticism.  PdSe,  19:  1912,  186-200. 

*59.  Anna  Schubert.  Versuch  einer  Anwendung  d.  System  v. 
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*60.  H.  Seifert.  Alfred  Binet  und  seine  Intelligenzprufung. 
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*61.  F.  C.  Shrubsall.  The  examination  of  mentally  defective 
children.  School  Hygiene  (London),  2:  1911,  No.  11. 


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62.  W.  Stern.  Fragestellungen,  Methoden  und  Ergebnisse  der 
Intelligenzprfifung.  (See  Reference  11.) 

*63.  L.  M.  Terman.  The  Binet-Simon  scale  for  measuring  intel- 
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206. 

*64.  L.  M.  Terman  and  H.  G.  Childs.  A  tentative  revision  and 
extension  of  the  Binet-Simon  measuring  scale  of  intelligence. 
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*65.  Z.  Treves  ed  U.  Safflotti.  La  'scala  metrica  dell'  intelli- 
genza'  di  Binet  e  Simon.  Nota  preventiva.  Milan  (Laboratorio 
civico  di  Ps.),  1910. 

*66.  Z.  Treves  ed  U.  Saffiotti.  La  'scala  metrica  dell'  intelli- 
genza'  di  Binet  e  Simon.  Studiata  nelle  Scuole  communali  elemen- 
tari  di  Milano.  Esposizione  e  critica.  Milan  (Labor  atorio  civico 
di  Ps.  pura  ed  applicata),  1911.  Pp.  67. 

*67.  J.  E.  W.  Wallin.  A  practical  guide  for  the  administration 
of  the  Binet-Simon  scale  for  measuring  intelligence.  PsCl,  5 :  1911, 
217-238 

*68.    J.  E.  W.  Wallin.    Human  efficiency.    PdSe,  18 :  1911,  74-84. 

*69.  L.  E.  Widen.  A  comparison  of  the  Binet  and  Simon 
method  and  two  discrimination  methods  for  measuring  mental  age. 
(Thesis.)  Iowa  City,  1911. 

C.    On  Part  III. 
(Rank-order  Method.    Correlation.    Teachers'  Estimates.) 

See  also  literature  cited  in  Reference  1,  pp.  391-392. 

70.  W.  Betz.  Ueber  Korrelation.  Methoden  d.  Korr.  Berech- 
nung  u.  krit.  Bericht  fiber  Korr. — Untersuchungen  a.  d.  Geb.  d. 
Intelligenz,  d.  Anlagen  u.  ihre  Beeinflussung  durch  aussere  Um- 
staiide.  Beihcft  zur  ZAngPs  (3),  1911.  Pp.  88. 

*71.  A.  Binet.  Comment  les  instituteurs  jugent-ils  1'intelligence 
d'un  ecolier?  Bull,  de  la  soc.  libre,  etc.  1910,  p.  172. 

72.  C.  Burt.  Experimental  tests  of  general  intelligence.  BrJPs, 
3 :  1909,  94-177. 

*73.  Alice  Descoeudres.  Exploration  de  quelques  tests  d'intelli- 
gence  chez  des  enfants  anormaux  et  arri£r£s.  ArdePs,  11:  1911, 
351-375. 

*74.  W.  H.  Gilby,  assisted  by  K.  Pearson.  On  the  significance 
of  the  teacher's  appreciation  of  general  intelligence.  Biometrika, 
8 :  1911,  94-108. 

*75.  B.  Hart  and  C.  Spearman.  General  ability,  its  existence 
and  nature.  BrJPs,  5 :  1912,  51-79. 

*76.  H.  Gertrude  Jones.  On  the  value  of  the  teacher's  opinion 
of  the  general  intelligence  of  school  children.  Biometrika,  1 :  1910, 
542-548. 


152   PSYCHOLOGICAL  METHODS  OF  TESTING  INTELLIGENCE 

77.  F.  Krueger  und  C.  Spearman.     Die  Korrelation  zwischen 
verschiedenen  geistigen  Leistungsfahigkeiten.     ZPs,  44:  1906,  50- 
114. 

78.  G.    Ries.     Beitrag   zur   Methodik   der    Intelligenzpriifung. 
ZPs,  56 :  1910,  321-343. 

79.  C.  Spearman.    The  proof  and  measurement  of  association 
between  two  things.    AmJPs,  15 :  1904,  72-101. 

80.  C.  Spearman.    'General  Intelligence'  objectively  determined 
and  measured.    AmJPs,  15 :  1904,  201-292. 

*81.  H.  Waite.  The  teacher's  estimation  of  the  general  intelli- 
gence of  school  children.  Biometrika,  8 :  1911,  79-93. 

Note :  Heft  5/6  of  ZAngPs,  Vol.  6,  which  contains  the  articles  of 
Bobertag  (40,  II),  Chotzen  (44)  and  Block  u.  Preiss  (38),  can  also 
be  purchased  separately  through  book  sellers. 


APPENDICES 


APPENDIX  I. 

Example  of  the  Computation  of  a  Correlation. 

Correlation  between  'class-place'  (x)  and  a  teacher's  estimate  of 
intelligence  (y). 

62  (»  —  I/)' 
Index  of  correlation  =  o  =  1  — 


n  (n'  — 


I  — 


Probable  error  =  P.  E.  =  .706 


Q 


(n  =  23  pupils  in  Untertertia — grade  entered  at  about  12  years.) 

Pupils  x  y  x  —  y  (x  —  y)1 

A  1  10  —  9  81 

B  2  14  —12  144 

C  3  13  —10  100 

D  4  1  +3  9 

E  5  5  00 

F  6  7  —   1  1 

O  7  20  —13  169 

H  8  2  +6  36 

I  9  8  +1  1 

J  10  15  —   5  25 

K  11  9  +2  4 

L  12  22  —10  100 

M  13  4  +9  81 

N  14  11  +3  9 

O  15  3  +12  144 

P  16  21  —   5  25 

Q  17  6  +11  121 

B  18  18  00 

S  19  12  +7  49 

T  20  16  +4  16 

U  21  23  —   2  4 

V  22  17  +5  25 

W  23  19  +4  16 

Sum    1160 
6.1160 


23  (23a  — 


=0.43. 


1  —  0.43s 

P.  E.  =  0.706  -  =0.12. 
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INDEX 


Abnormal  adults,  6.  Descoeudres,  Alice,  48,  68,  96, 

Abnormal  children,  6f.,  41,  66,       141f. 

70-91.  Dieffenbacher,  65,  98. 

Ayres,  47,  92.  Discrimination,  tests  of,  136. 

Dosai-RSv§sz,  M.,  75. 


Bell,  J.  C.,  94f. 

Bernstein,  6,  16. 

Binet,  A.,  8,  17,  19,  29,  31,  34, 
36f.,  43,  47,  49,  53,  59,  61,  72, 
76,  90,  95,  98,  100,  103,  118. 

Binet-Simon  method,  10f.,  26; 
principle  of,  29-36;  resultant 
values  in,  36-42 ;  technique  of, 
34ff. ;  sex-differences  in,  65- 
68;  improvement  of,  91-108; 
composition  of  age-levels  in, 
99-101;  extension  of,  101-104. 

Bloch,  E.,  47,  66ff. 

Bobertag,  O.,  12,  29,  31,  36,  39, 
43,  45-48,  50,  60ff.,  68f.,  72,  79, 
84f.,  87,  94ff.,  101,  103f. 

Bourdon  test,  17. 

Breslau,  experiments  at,  35,  50, 
54-57,  71,  129. 

Brussels,  experiments  at,  50. 

Burt,  C.,  128,  135,  140. 

Childs,  H.,  31,  34,  48,  94f.,  102, 

105. 
Chotzen,  F.,  34,  66,  71,  73,  80ff., 

76ff.,  85,  97f. 
Cohn,  65,  98. 
Compensation,      principle      of, 

113ff.,  139f. 
Completion  test,  7,  15f.,  20,  65, 

102,  110. 

Contingency,  method  of,  59f. 
Correlation   method,    10f.,   26f., 

lllff.,  135-143. 


Decroly,  O.,  50,  53. 
Degand,  J.,  50,  53. 


Ebbinghaus,  H.,  7,  15f.,  20,  65, 
102,  110;  see  completion  test. 

Estimation  of  intelligence,  10, 
115-144. 

Feeble-minded,  66,  141f. ;  see 
abnormal  children. 

Galton,  F.,  45. 

Gauss'  curve,  45. 

General  intelligence,  112f. 

Genius,  4. 

Gilby,  W.  H.,  128. 

Goddard,  H.,  43,  46ff.,  59,  60,  62, 
65,  71ff.,  95. 

Gradation,  method  of,  see  Binet- 
Simon  method. 

Gregor,  6. 

Hart,  B.,  11. 
Heilbronner  test,  16. 
Huey,  E.  B.,  36. 
Hylla,  136,  140. 

Imbecile,  70,  74,  81,  83;  see 
moral  imbecile. 

Information  tests,  6. 

Intelligence,  nature  of,  2-5,  9, 
15,  17,  20f.,  113ff.,  120;  gen- 
eral distribution  of  level  of, 
43ff. ;  rank-orders  of,  135-143. 

Intermediate  ages,  103. 

Irregularity,  area  of,  37,  39,  85. 

Jaspers,  K.,  6. 
Johnstone,  K.  L.,  47f.r  95. 
Jones,  H.  G.,  128. 


159 


160   PSYCHOLOGICAL    METHODS  OP   TESTING    INTELLIGENCE 

Kattowitz,  investigations  at,  66.  Repetition   of   tests,    effect   of, 

Kraepelin,  6.  68ff. 

Kramer,  F.,  9,  64,  71,  75f.,  79,  Report  experiment,  7. 

90f.  Rieger,  6,  23. 

Ries,  G.,  16,  135-139. 

Levistre,  95.  Rindfleisch,  129. 

Lipmann,  O.,  14,  36.  Rodenwald,  E.,  6. 

Rossolimo,  6,  16,  25f. 
Masselon  test,  16,  99. 

Mental  advance,  41,  44,  59ff.,  69.  Saffiotti,  36. 

Mental  age,  41 ;  computation  of,  Scattered  distribution,  area  of, 

37ff.,  104-108.  35. 

Mental  arrest,  42,  70-84.  Scheifler,  129. 

Mental  quotient,  42,  79-84,  101,  School  activities  as  tests,  17f. 

103,  105f.  School     standing     and     intelli- 

Mental  retardation,  41,  44,  59ff.,  gence,  57-65,  90f.,  110,  127-135. 

69-84.  Series  of  tests,  13f.,  23-27. 

Meumann,  E.,  6,  9,  16f.,  29,  98f.  Sex-differences,  65-68. 

Meyer,  llf.,  65.  Simon,  8,  29,  31,  34,  36f.,  49,  100. 

Moral  imbecile,  74f.  Single  tests,  13-23,  135. 

Morl£,  M.,  95.  Social  differences,  50ff. 

Moron,  70,  73,  801,  83.  Sommer,  R.,  6f.,  23. 

Miinsterberg,  H.,  10.  Spearman,  C.,  10f.,  21,  112f. 

Myers,  C.  S.,  12.  Special  classes,  9,  71,  90. 

Stern,  W.,  13f.,  45,  52. 

Nationality,  effect  of,  49.  Subnormal  Children,  see  abnor- 

Nicolauer,  M.,  71.  mal    children,    feeble-minded, 

Normal  children,  results  with,  special  classes. 

42-70. 

Talent,  4,  10. 

Parallel  series  of  tests,  102.  Teachers'    estimates,    see    esti- 

Paris,  experiments  at,  51f.  mation. 

Pearson,  K.,  10f.,  128.  Terman,  L.,  34,  48,  94f.,  102,  105. 

Pedagogical     age,     58ff. ;     see  Treves,  36. 

school  standing. 

Preiss,  A.,  47,  66ff.  Vineland,  experiments  at,  71. 

Profile  method,  25f.  Volksschule,     experiments     in, 

Psychiatrists,  6f.,  18,  23.  54-57,  66ff,  96,  129. 

Qualitative   analysis   by   Binet-  Waite,  H.,  128. 

Simon  method,  85-90.  Wallin,  J.,  12,  36. 

Weintrob,  J.  and  R.,  52. 

Rank-order,  method  of,  109-144 ;  Whipple,  G.  M.,  7,  12,  14,  36. 

rules  for  forming,  120-127.  Winteler,  J.,  16,  98. 

Ranschburg,  7.  Wreschner,  65. 
Ranschburg  method,  137. 

Reliability  of  tests,  69,  142.  Ziehen,  T.,  6f.,  23. 


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